Method for correcting unadjusted threshold arrays for halftoning by use of parameterized transfer functions that generate adjusted threshold arrays at run time

ABSTRACT

A printer that stores a minimal number of unadjusted stochastic threshold arrays in non-volatile memory, in which the unadjusted threshold arrays are used to generate adjusted threshold arrays at run time by use of special parameterized transfer functions. The unadjusted array for a particular color is stored in the printer&#39;s ROM and preferably is stored in a packed configuration to save memory space. The parameterized transfer functions are used to convert the unadjusted threshold data into adjusted threshold data for each color and type of print media. These parameterized transfer functions are stored in the printer&#39;s non-volatile memory, and take up very little memory space. In a preferred embodiment, the unadjusted threshold array comprises a 128 row by 128 column sized array, and each element of this array comprises a 10-bit number. When a parameterized transfer function is applied to this unadjusted array, the resulting numeric values for the adjusted array elements are produced as 8-bit numeric values. The greater precision in the originating unadjusted array provides more perceptual levels of intensity (i.e., color brightness), which is particularly important at the lighter shades of each color. The adjusted threshold arrays add only the number of dots per gray level (i.e., per differential threshold array level) that are required to provide a printer response that very nearly approximates the human eye perceptual differential response of intensity.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a divisional to application Ser. No. 09/442,211, titled “METHOD AND APPARATUS FOR CORRECTING UNADJUSTED THRESHOLD ARRAYS FOR HALFTONING BY USE OF PARAMETERIZED TRANSFER FUNCTIONS THAT GENERATE ADJUSTED THRESHOLD ARRAYS AT RUN TIME,” filed on Nov. 17, 1999 now U.S. Pat No. 6,512,597.

TECHNICAL FIELD

The present invention relates generally to image forming equipment and is particularly directed to printers of the type which halftone color or black and white images. The invention is specifically disclosed as a printer that provides a 10-bit unadjusted stochastic threshold array, and applies one or more parameterized transfer function equations at run time to the unadjusted array to derive an 8-bit adjusted threshold array, thereby improving perceptual printer response while saving memory space.

BACKGROUND OF THE INVENTION

Threshold arrays have been used for years to accomplish halftoning for image forming equipment, such as printers. Modem printers generally use a threshold array in a tiling manner to halftone a particular square or rectangular portion of an image bitmap that is to be printed, and then move the threshold array to the next position as if placing a new tile over the bitmap in an adjacent location. Video displays also can operate using tiled threshold arrays. Threshold arrays include array elements that have numeric values that range from the lightest gray scale shade to the darkest gray scale shade. As the light intensity (or a particular color intensity) increases, a greater number of pixels will be illuminated in a display device such as a liquid crystal display, or conversely a fewer number of dots will be printed in the case of a printer as the output device. This is accomplished by comparing the actual pixel intensity values against the array element numeric values. For example, all dots will be printed for threshold levels at array element locations that have a numeric value less than the dot intensities of the input image information.

The numeric values of the array elements for threshold arrays in conventional printers are normally integer values that define a plurality of gray levels, and the most typical range of numeric values is from 0 through 255, which are represented by 8-bit binary numbers. Since 8-bit linear or unadjusted threshold arrays produce printed responses that typically do not match the desired linear human perceptual response, it has been common for most printers to provide adjusted (or corrected) threshold arrays for each color that can be printed by that particular print engine. In color printers, for example, this implies that there would be a minimum of three different adjusted threshold arrays for the “ordinary” colors cyan, magenta, and yellow, and further, many color printers also provide black ink, thereby requiring a fourth adjusted threshold array. (Some printers may provide a single threshold array to be used for all colors, but the visual results are not pleasing.) Such adjusted threshold arrays may have array elements of integer numeric values or, to achieve greater precision, the numeric values could each be represented by a floating point number. Floating point values will require, of course, much more storage space in the memory system of a printer than the use of integer values. One main reason that 8-bit integer values are typically used for the gray level representations is that standard memory devices provide “chunks” of memory in bytes, which each comprise a set of 8 bits.

Early printers may have used unadjusted threshold arrays to produce their final printed outputs, however, such printers usually lose tone levels, and at best exhibit crude approximations to the desired perceptual tone levels. While some print engines may produce reasonable perceptual responses by use of unadjusted threshold arrays, that is not the general case, and adjusted threshold arrays are much more common.

To develop a linearized halftone screen, it is common to start with a grid of equal proportions of the numbers between one (1) and the maximum value, and then print squares representing each of the tone levels. The printed squares can be then measured with respect to the parameter that is desired to be linearized. The series of measured values can then be assembled and analyzed to form an adjusted (or corrected) halftone screen or threshold array that is linear. The new screen or array is formed for a given paper type, color plane, printing mechanism, etc., and usually is stored in ROM to be used when printing.

The maximum value of the equal proportions used in generating the unadjusted threshold array may not be the same as the maximum tone level. However, the maximum values of the adjusted screen or threshold array and the tone level must be the same. It very rarely occurs that using an unadjusted screen yields a set of equally visually spaced discernible intensity levels, which is the property of a “perfect” halftone screen. Thus, it is necessary to “correct” (or adjust) this screen.

In correcting the screen (or threshold array), the first thing to be achieved is determining a set of distinct intensity levels, as many as the number of tone levels (i.e., gray scale levels in many cases). These intensity levels must be analyzed and modified so that they are as visually distinct as possible. This usually is done by linearizing the screens in L* space. Historically, correction (or adjustment) of the screens or threshold arrays has been done using one of two different methods. The first method is referred to as the “array mapping” method, which stores a one-dimensional array that maps each of the possible values in the uncorrected (or unadjusted) screen or threshold array to the appropriate value in the corrected (or adjusted) screen or threshold array. Each of the values in the unadjusted screen or threshold array is used as an index to the array map, and the adjusted screen or threshold array is formed therefrom. This method saves memory space, but can be restrictive concerning the number of dots that must be placed on the page for different tone levels. For example, if the uncorrected (or unadjusted) screen or array has dimensions of 128×128, and if there are 256 tone levels, each tone level must contain 64 more dots than the previous level, assuming that the unadjusted screen or array contains equal proportions of each value (which must be true if it is to be used as a base to transition to adjusted (or corrected) arrays).

Since being restricted to adding a fixed number of dots at each level reduces the number of distinct intensity levels, accuracy will suffer. This accuracy problem can be alleviated by increasing the range of values in the unadjusted screen or array until the maximum number of unique levels is obtained. Unfortunately, this also increases the size of both the one-dimensional arrays and the unadjusted screens, which are both stored in the printer when using the array mapping method. The size of the one-dimensional arrays increases proportionally with the bit size of the uncorrected (or unadjusted) screens or threshold arrays.

The second historical correcting method is called the “complete storage” method. This performs the complete correction of the threshold arrays offline, and all of the adjusted (or corrected) threshold arrays are stored in the ROM of the printer. No correction takes place at run time. This method requires a large amount of memory space; however, it's advantage it that the adjusted (or corrected) threshold arrays can be manipulated as necessary to obtain the greatest number of visually discernible intensity levels, since all correction is done offline (i.e., at the factory). Increase of accuracy does not mean an increase of the memory space required for storage. Nevertheless, the memory storage space is quite large for any threshold arrays of meaningful precision.

In printers that provide adjusted threshold arrays, a separate transfer function is typically determined for each color that can be printed, and additionally, for each type of print media that will be printed on. The benefits of using adjusted threshold arrays include assuring that there will be 256 unique tone levels (e.g., for 8-bit integer gray levels), and further, to produce tone levels as close as possible to each desired perceptual level. However, a separate array must be generated for each combination of color and type of paper, and therefore, a large amount of memory is required to store each of the separate, adjusted threshold arrays. More detailed examples of the memory requirements are provided hereinbelow.

Once the printer's actual response curve is known, it is possible to apply a transfer function to correct or adjust the data so that a perceptually appropriate gray level will be printed for a corresponding lightness level L*. In the prior art, such transfer functions have normally taken the form of a correction factor that is added to the gray level for a particular lightness L* value. In essence, the printer's response curve (such as curve 102 on FIG. 2) is compared to the ideal target response (such as line 100 on FIG. 2), and the deviation at all important points is calculated. Once this deviation is known, it is a simple matter to create a mirror-image curve on the opposite side of the ideal target response line 100, and this mirror-image curve can be added to the actual printer response curve (such as curve 102) and an average taken, which then will provide the adjusted (or corrected) response that will have the appearance of the ideal target response line 100.

While the prior art methodology works well for many conventional printers, a large amount of memory storage space is required to store the corrected threshold array that is generated or derived by applying the mirror image transfer function curve to correct for the printer's non-linear actual response curve. Moreover, since correcting for each printer color and print media type will lead to a large number of possible combinations, it has been common in the prior art for the conventional printers to store a large number of such adjusted threshold arrays in their non-volatile memory, such as in the printer's ROM, thereby requiring substantial amounts of memory space.

Since threshold arrays provide an extremely fast way to halftone an image, various types of halftoning techniques have been developed that all use threshold arrays, including cluster-dot ordered dithering (known as “classical” screening), dispersed-dot ordered dithering (known as “Bayer” screening), dispersed-dot unordered dithering (known as stochastic screening), or another form of stochastic screening, using cluster-dot unordered dithering. For printers that must quickly process image data for an incoming print job, this extremely fast method using threshold arrays so far seems to be the optimum method to halftone various types of images. It would be very beneficial to further streamline the process of providing corrected threshold arrays, especially when that process can also save memory space within the printer's memory circuits.

SUMMARY OF THE INVENTION

Accordingly, it is a primary advantage of the present invention to provide an image forming apparatus such as a printer that stores a minimum number of threshold arrays in non-volatile memory, and at run time creates adjusted threshold arrays to meet the precise print job requirements, such as for the appropriate colors and appropriate types of print media.

It is another advantage of the present invention to provide an image forming apparatus such as a printer that stores a minimal number of unadjusted threshold arrays consisting of numeric elements that have a greater precision than the numeric elements of adjusted threshold arrays that are derived at run time and which benefit from the greater precision of the unadjusted arrays to more nearly match the printer's response to the human visual perceptual levels.

It is a further advantage of the present invention to provide an image forming apparatus such as a printer that stores a minimal number of unadjusted threshold arrays consisting of numeric elements that have a greater precision than the numeric elements of adjusted threshold arrays that are derived at run time and which benefit from the greater precision of the unadjusted arrays to create a predetermined non-linear response that closely matches a response of another printing device, as desired for a specific printing application.

It is a yet further advantage of the present invention to provide an image forming apparatus such as a printer that stores a minimal number of unadjusted threshold arrays and generates adjusted threshold arrays that are derived at run time and which compensate for the gradual change in darkness of the printer response due to the aging of an electrophotographic (EP) process cartridge over its useful life, by providing new transfer functions that further correct the adjusted threshold arrays after predetermined amounts of usage of the EP process cartridge.

It is yet another advantage of the present invention to provide an image forming apparatus such as a printer that stores a minimum number of unadjusted threshold arrays along with a set, of transfer function equations that can quickly produce a set of adjusted threshold arrays that are minimal in number to reduce memory requirements, and further that are produced for the specific print job requirements, such as the appropriate colors to be printed as well as the type of print media to be printed upon.

It is still a further advantage of the present invention to provide an image forming apparatus such as a printer that stores a minimal number of unadjusted threshold arrays in a packed memory configuration to minimize the amount of memory space required in a non-volatile memory circuit, and to provide an unpacking routine that quickly re-configures the unadjusted threshold array data in a format that allows quick access and application of a set of transfer function equations to derive a set of adjusted threshold arrays to be stored in the printer's RAM circuit.

It is still another advantage of the present invention to provide an image forming apparatus such as a printer having a minimal number of unadjusted threshold arrays stored in a printer's non-volatile memory circuit in a packed data format to minimize the amount of space required in the printer's ROM storage circuit, and to provide an unpacking routine that quickly unpacks the unadjusted threshold array data, and applies one or more transfer function equations that generate a set of adjusted threshold arrays at run time, in which these adjusted threshold arrays are generated for the precise print job requirements, such as appropriate colors and type of print media to be printed upon.

It is yet a further advantage of the present invention to provide a set of packed data stochastic threshold arrays that are stored in a printer's non-volatile memory circuit, in which these threshold arrays comprise array elements having numeric values of a greater precision than the precision of numeric elements for later derived adjusted threshold arrays that are generated at run time by the printer after application of a set of transfer function equations that convert the unadjusted threshold arrays into adjusted threshold arrays.

Additional advantages and other novel features of the invention will be set forth in part in the description that follows and in part will become apparent to those skilled in the art upon examination of the following or may be learned with the practice of the invention.

To achieve the foregoing and other advantages, and in accordance with one aspect of the present invention, an improved printer is provided that stores a minimal number of unadjusted stochastic threshold arrays in non-volatile memory, in which a single stochastic threshold array is provided per ordinary color of the printer. For example, if the printer is a black and white printer only, then only a single stochastic threshold array would be required. This single unadjusted array is used to determine the printer's light intensity printed response, which will not likely provide an ideal target response as compared to the perceptual intensity levels of the human eye. Accordingly, the uncorrected threshold array needs to be adjusted before the array is used to halftone image data in the form of a print job.

The unadjusted array for a particular color is stored in the printer's ROM (Read Only Memory) and preferably is stored in a packed configuration to save memory space. A set of transfer function equations (also referred to herein as “parameterized transfer functions”) additionally are provided for the various types of print media that can be expected for use with a particular printer, as well as for various combinations of ordinary colors and specialized colors. For example, if the uncorrected threshold array represents the color magenta, and if the print media type is “plain paper,” and further if the type of printing that is to be accomplished is to use the “ordinary” magenta shading, then either a single transfer function equation, or multiple transfer function equations, is/are applied to the unadjusted threshold array, which produces a single corrected threshold array that will be the “target array” for halftoning the color magenta when printing this particular print job. On the other hand, if a “diluted” magenta color ink is to be utilized (for example, if a color “photo cartridge” is used in a particular style of ink jet color printer), then a different set of transfer function equations will be applied to the unadjusted threshold array to produce a different adjusted threshold array (i.e., for diluted magenta ink) that will finally be used at run time to halftone this particular print job. This is just one example of the various combinations of color shades and print media types that can be utilized with a modem color printer.

The mere use of unadjusted threshold arrays will typically produce printed shades that are too dark as compared to the incremental shade differences as perceived by the human eye. The transfer function equations are used to convert the unadjusted threshold data into adjusted threshold data for each color and type of print media. In a preferred embodiment, the particular transfer function equations generate a temporary conversion table which essentially acts as a look-up table in which the original numeric value of a particular array element in the unadjusted threshold array is found, and a different numeric value is then substituted therefor. In short, for every array element position in which the original numeric value appeared, a corrected numeric value is then substituted in the same row and column position of the derived, adjusted threshold array. This occurs very quickly at run time for each print job received by the printer that requires halftoning.

As an alternative embodiment, the transfer function equations can be applied to each single data element of the unadjusted threshold array, and a new “corrected” data value can be calculated and placed into the appropriate memory element location in the adjusted threshold array now being derived. In this alternative methodology, a temporary look-up table is not needed, which saves some space in the printer's RAM that otherwise would need to be temporarily allocated. However, in this alternative methodology, the execution or processing time to derive the adjusted threshold array in this manner—that is, by inspecting each numeric value of the unadjusted threshold array and then applying the correct transfer function equation for the correct range of gray scale values to calculate the corrected numeric value in the adjusted array—will likely be greater than that of the preferred methodology described above. It should be noted that multiple calculations for the very same numeric value will be the result of applying the alternative methodology in circumstances where the unadjusted threshold array is of a sufficient size, i.e., if its size requires the same threshold level numeric value in multiple array element locations.

In the preferred mode of the present invention, the unadjusted threshold array comprises a 128 row by 128 column sized array, and each element of this array comprises a 10-bit number having a precision of one part in 1024. When the transfer function equations are applied to this unadjusted array, the resulting numeric values for the adjusted array elements are produced as 8-bit numeric values, which provides a somewhat lower precision of one part in 256. This greater precision in the originating unadjusted array provides more perceptual levels of intensity (i.e., color brightness), which is particularly important at the lighter shades of each color. This greater number of possible printed gray levels by using the 10-bit numeric data is used to advantage, and the adjusted threshold arrays derived therefrom will add only the number of dots per gray level (i.e., per differential threshold array level) that are required to provide a printer response that very nearly approximates the human eye perceptual differential response of intensity. In essence, the 8-bit adjusted threshold arrays used in printing the colors effectively have the precision of 10-bit data.

Since most modern microprocessor and memory circuits are based upon 8-bit bytes, use of 10-bit data normally requires a 2-byte data word for storage in the memory circuit. Such 2-byte data words are easily accessed for each individual 10-bit data numeric value. However, in the preferred embodiment of the present invention, the unadjusted threshold arrays are stored in a packed data format, such that contiguous memory locations are used to store each 10-bit numeric value with no unused bits spaced therebetween (e.g., such as “padding bits” used to round the data size up to two bytes per value). This saves over 35% of the memory space in the printer's non-volatile memory required for storing the unadjusted threshold arrays.

At run time, it is preferred to unpack this 10-bit data for the unadjusted threshold arrays by removing each 10-bit numeric value from the packed memory locations and placing it into a different 2-byte set of memory locations, which then makes it very easy to access this 10-bit data value merely by scrolling through the various memory locations. The appropriate transfer function equations are then applied to each unadjusted threshold array, and the output of this transfer function equation application is an 8-bit numeric value for each array element in the derived adjusted threshold array that will be used for printing that particular color/media combination. Since the adjusted threshold array uses 8-bit numeric data, this will perfectly correspond to a single byte of memory space, thereby most efficiently packing this adjusted array data.

The principles of the present invention can be applied to any type of unadjusted threshold arrays, regardless of how they are derived (e.g., stochastic, dot-cluster, etc.). Moreover, the present invention will produce a memory savings in the printer regardless of the data size of the unadjusted threshold arrays and the resulting adjusted threshold arrays, by use of the transfer function equations as described hereinbelow. Furthermore, the present invention can be used to advantage regardless of whether or not the data is packed or unpacked, since both a memory storage space savings is exhibited, as well as an increase in efficiency by using less processing time to derive the adjusted threshold arrays at run time, as compared to other methodologies. Finally, the present invention can be used to advantage to provide corrected threshold arrays regardless of the shape of the response curves of any of the colors when utilizing a particular print engine's response curve for its unadjusted threshold array data.

The principles of the present invention not only apply to printers, but also apply equally well to other types of image forming apparatuses including copiers and video displays that use halftoning techniques. Of course, many video monitors do not require halftoning, since they can be designed to directly apply the correct intensity of the individual primary colors for each pixel. However, certain types of video displays may well require halftoning for a correct or pleasing visual appearance of images. Such video displays include liquid crystal displays (LCD's) and light emitting diode (LED) displays. Moreover, even some cathode ray tube (CRT) displays may use halftoning, especially for older such CRT's.

The principles of the present invention further apply not only to situations where the printer's response is being corrected so as to appear “linear” in accordance with human visual perception, but also to situations where the printer's response is purposely being corrected so as to appear “non-linear” in accordance with a customer/user's printing application. Moreover, the principles of the present invention can be used to compensate for the gradual change in darkness in the printer response due to aging of components of EP-type printers (including components of EP process cartridges). A new set of transfer function equations can be applied to create a new set of adjusted threshold arrays after predetermined amounts of usage of the EP process cartridge, or other internal printer components.

Still other advantages of the present invention will become apparent to those skilled in this art from the following description and drawings wherein there is described and shown a preferred embodiment of this invention in one of the best modes contemplated for carrying out the invention. As will be realized, the invention is capable of other different embodiments, and its several details are capable of modification in various, obvious aspects all without departing from the invention. Accordingly, the drawings and descriptions will be regarded as illustrative in nature and not as restrictive.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings incorporated in and forming a part of the specification illustrate several aspects of the present invention, and together with the description and claims serve to explain the principles of the invention. In the drawings:

FIG. 1 is a block diagram of the major components of a printer, as constructed according to the principles of the present invention.

FIG. 2 is a graph illustrating the printer response for a single color showing actual darkness versus gray level, as well as the ideal target response, and further depicts a set of transfer function equations calculated to “fit” the printer response curve, as according to the principles of the present invention.

FIG. 3 is a graph illustrating an actual printer response for printing on three different types of paper, showing print darkness versus gray level, as well as their ideal target response for those three paper types.

FIG. 4 is a flow chart depicting initial set-up steps for determining the printer response for each color, then generating one or more transfer function equations for each color that will be used to derive an adjusted threshold array used in halftoning, as according to the principles of the present invention.

FIG. 5 is a flow chart depicting the steps for packing data into a very tight memory structure, as according to the present invention.

FIG. 6 is a flow chart depicting the steps for unpacking data from a very tight memory structure, as according to the present invention.

FIG. 7 is a flow chart illustrating the steps for applying a temporary look-up table generated from application of transfer function equations to an unadjusted threshold array, as according to the methodology of the present invention.

FIG. 8 is a flow chart illustrating the steps for both unpacking the corrected array data and applying a temporary look-up table, generated from application of transfer function equations to an unadjusted threshold array, in a single step for each value of the adjusted array, as according to the principles of the present invention.

FIG. 9 is a graph illustrating a histogram of threshold values versus the number of occurrences in a 32×32 array that was corrected from an 8-bit threshold array, as according to the present invention.

FIG. 10 is a graph illustrating a histogram of threshold values versus the number of occurrences in a 32×32 array that was corrected from a 10-bit threshold array, as according to the principles of the present invention.

FIG. 11 is a flow chart illustrating the steps for sampling the transfer function equations and applying them to the uncorrected data of the unadjusted threshold array in order to derive the adjusted threshold array, according to the principles of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Reference will now be made in detail to the present preferred embodiment of the invention, an example of which is illustrated in the accompanying drawings, wherein like numerals indicate the same elements throughout the views.

Referring now to the drawings, FIG. 1 shows a hardware block diagram of a laser printer generally designated by the reference numeral 10, although virtually the same components will be found on many ink jet printers. Laser printer 10 will preferably contain certain relatively standard components, such as a DC power supply 12 which may have multiple outputs of different voltage levels, a microprocessor 14 having address lines, data lines, and control and/or interrupt lines, Read Only Memory (ROM) 16, and Random Access Memory (RAM) 15, which is divided by software operations into several portions for performing several different functions.

Laser printer 10 also contains at least one input port, or in many cases several types of input ports, as designated by the reference numeral 18. Each of these ports would be connected to a corresponding input buffer, generally designated by the reference numeral 22 on FIG. 1. Each port 18 would typically be connected to an output port of either a personal computer (PC) or a workstation (WS) (designated on FIG. 1 as an “input device” 24) that would contain a software program such as a word processor or a graphics package or computer aided drawing package, or to a network that could be accessed by such a PC or WS. Laser printer 10 preferably will also contain an Application Specific Integrated Circuit (ASIC) 20, which typically contains a large number of programmable logic circuits.

Once text or graphical data has been received by input buffer 22, it is commonly communicated to one or more interpreters designated by the reference numeral 28. A common interpreter is PostScript™, which is an industry standard used by many laser printers. To speed up the process of rasterization, a font pool and typically also a font cache are stored in memory within most laser printers, and these font memories are designated by the reference numeral 32, 33, 50 and 52 on FIG. 1. Such font pools and caches supply bitmap patterns for common characters so that a graphics engine 30 can easily translate each such character into a bitmap using a minimal elapsed time. The memory devices designated by the reference numerals 50 and 52 may be options on most laser printers, in which a hard disk drive 50 and/or a Flash memory device 52 can be added to the base printer upon the request of the user/customer. Such alternative storage memory devices also will likely appear in top-line ink jet printers in the future.

Once the data has been rasterized, it is directed by a page queuing system 34 into a page buffer, which is a portion of RAM designated by the reference numeral 35. In a typical laser printer, an entire page of rasterized data is temporarily stored by the page queuing system 34 in the page buffer 35, although some of the more modem laser printers do not buffer an entire page's worth of data at one time, thereby managing to operate with a much smaller amount of RAM in a “partial page buffer.” The data within the page buffer 35 is communicated in real time to a print engine designated by the reference numeral 36. Print engine 36 includes a laser light source within its printhead (not shown), and its output 40 is the physical printing onto a piece of paper, which is the final print output from laser printer 10. Print engine 36 also may contain a programmable non-volatile memory device 42, in addition to registers contained within its ASIC 44 that may act as either RAM or ROM, as desired. Programmable memory device 42 could consist of a Flash type-device, or an NVRAM-type device, for example, or any other type of non-volatile memory device. Of course, certain printer-specific information could be stored within the programmable memory device 42, and preferably this information can be updated from a host computer (e.g., input device 24) if desired. This concept will be discussed in greater detail hereinbelow, as applicable to the present invention.

It will be understood that the address, data, and control lines are typically grouped in buses, which are electrically conductive pathways that are physically communicated in parallel (sometimes also multiplexed) around the various electronic components within laser printer 10. For example, the address and data buses are typically sent to all ROM and RAM integrated circuits, and the control lines or interrupt lines are typically directed to all input or output integrated circuits that act as buffers. For ease of illustrating the present invention, the various buses used within printer 10 are grouped on FIG. 1 into a single bus pathway, designated by the reference numeral 11.

A portion of the RAM 15 is typically allocated for virtual memory for at least one interpreter, and on FIG. 1 a POSTSCRIPT virtual memory is depicted at the reference numeral 31. This virtual memory 31 can, for example, be used for storing PostScript font descriptors within the printer. In addition, particularly important information that is to be retained in printer 10 while unpowered can be stored in a quickly accessible non-volatile memory location called “NVRAM,” which is designated by the reference numeral 26. This non-volatile RAM is most likely (using today's technology) an EEPROM integrated circuit chip.

A replaceable cartridge, generally designated by the reference numeral 60, is used in typical printing devices available at the present time. For ink jet printers, reference numeral 60 represents one or more ink cartridges that contain the black or colored ink that is supplied to the ink jet nozzles of the print engine 36. In many modem ink jet printers, a black ink cartridge is supplied separately from a colored ink cartridge that contains the standard “process” colors of cyan, magenta, and yellow ink. For laser printers (or other types of electrophotographic printing devices), reference numeral 60 represents a replaceable EP process cartridge that contains toner material, as well as a new photoconductive drum unit (not shown) supplied in most such EP process cartridges. The EP process cartridge typically contains black toner material for monochrome laser printers, and at least three different toner materials for color laser printers (for the standard “process” colors of cyan, magenta, and yellow—and possibly black), although multi-color EP printers and copiers are also available that use multiple individual toner cartridges that each contain only a single color of toner material. Whether or not a black toner cartridge—or a black toner “bay” of a multi-color EP process cartridge—is included for the particular printer or copier is a matter of design choice.

Some conventional EP process cartridges contain a non-volatile memory device, such as an EEPROM chip or an EPROM chip. For purposes of the present invention, the cartridge 60 contains a non-volatile memory device 62 that is programmable. Programmable memory device 62 could consist of a Flash type-device, or an NVRAM-type device, for example, or any other type of non-volatile memory device.

It is preferred to be able to update the stored information contained in this memory device 62. On the other hand, a write once, read often memory device could be used in conjunction with the present invention in a situation where the information stored therewithin is specific to certain characteristics of this particular cartridge 60. For example, in a laser printer one EP process cartridge 60 could provide a certain type of toner material that produces a particular response curve vs. intensity level of the image data, whereas a second, later design EP process cartridge 60 could provide a somewhat different type of toner material that produces a different particular response curve vs. intensity level of the image data. Such characteristics could be stored on memory device 62 and reported to the print engine 36 when the EP process cartridge 60 is installed into the main printer body of printer 10. Other types of data could also be stored on the memory device 62, as will be described in greater detail, hereinbelow.

In another example, in an ink jet printer one color toner cartridge 60 could provide a certain type of color inks that produce a particular response curve vs. intensity level of the image data, whereas a second color toner cartridge 60 could provide a somewhat different type of color inks (e.g., “dilute” colors) that produces a different particular response curve vs. intensity level of the image data. Such characteristics could be stored on memory device 62 and reported to the print engine 36 when the toner cartridge 60 is installed into the main printer body of printer 10. Other types of data could also be stored on the memory device 62, as will be described in greater detail, hereinbelow.

On FIG. 2, the line 100 represents the ideal target response for a printer that produces an output using gray level halftoning between its darkest possible output (as at the reference numeral 106) and its lightest possible output (as at the reference numeral 104). On FIG. 2, the gray levels are represented by 8-bit binary numbers ranging between zero (0) and 255. In this example, zero (0) represents the lightest gray level shade, while 255 represents the darkest gray level shade.

If the printer mechanism were ideal, then the printer's output (or “response”) would directly follow the line 100 between the lightest L* light intensity level at 104, and the darkest L* light intensity level at 106. FIG. 2 represents actual printer data for an ink jet printer that is printing the color magenta. On “plain paper” the lightest possible shade shows up as an L* value of 94.8 (which is blank paper), while the darkest possible shade is represented as an L* value of 46.1. Since the printer cannot create any darker L* value, there is no point in attempting to correct for values less than L*=46.1 (or above L*=94.8, which is due strictly to the paper brightness).

Since the vast majority of printers do not have an ideal response, it is preferred that their output responses be adjusted or corrected. Using the actual print data depicted along the curve 102, it can be seen that the example printer quickly produces light intensities for the color magenta that are much too dark as compared to the ideal response at line 100. In other words, the printer is simply producing too many dots at each incremental gray level after departing from the lightest possible point on the curve at L*=94.8 (at the reference numeral 104), which of course, is where no dots at all were printed. The curve 102 was generated by increasing the number of dots per gray level at a constant differential number of dots per next increasing gray level. This produces the unadjusted (or uncorrected) gray level response, as exhibited by the curve 102.

Unless some type of correction is applied to the printer's output, the printer's colors will always appear to be too dark with respect to the human eye's perceptual level. This is not only true with the single color magenta, but is also true for other colors on the vast majority of printers. Therefore, not only must the single color magenta be corrected, but all of the other printing primary (or “ordinary”) colors must be corrected, which typically would include cyan, yellow, and black. Each of these individual colors will have an individual response curve of L* versus gray level, although in the case of the color yellow, the preferred response curve to be analyzed and corrected for would be the b* curve versus gray level. It will be understood that the variables L* and b* refer to the CIELAB industry standard using the L*a*b* color space terminology.

Not only are the response curves for various colors different from one another for a particular printer, but additionally the color response for different types of print media also generate different curves on the L* or b* versus gray level graphs. For example, on FIG. 3 the three different curves, 102, 112, and 122, represent the printer response for the color magenta on three different types of paper. The curve 102 is the same as the curve seen on FIG. 2, and is for “plain paper.” The curve 112 also represents the printer's actual response for the color magenta, however, in this case the print media is “coated paper.” Finally, the curve 122 also represents the printer's actual response for the color magenta, although in this case the print media is “glossy paper.”

As can be seen by viewing FIG. 3, each of these curves 102, 112, and 122 not only has a different shape, but also has different starting and stopping points between the lightest shades at the gray level zero (0) and the darkest shades at the gray level 255. As was seen on FIG. 2, the curve 102 had a lightest end point at 104 and a darkest end point at 106, and the ideal target response was the line 100 between those two points. For the coated paper example, the curve 112 has its lightest shade end point at 114 and its darkest shade end point at 116, and the ideal target response is represented by the line 110 between those two points. Finally, the glossy paper example of curve 122 has its lightest shade end point at 124 and its darkest shade end point at 126, with an ideal target response line 120 between those two points.

The present invention eliminates the need for storing a large number of adjusted threshold arrays in a printer's non-volatile memory, such as its Read Only Memory (ROM). This can be a significant savings in memory, as will be described in greater detail hereinbelow. In the present invention, it is preferred to store only a single unadjusted threshold array for each of the ordinary colors that can be printed by a particular printer. If the printer is a monocolor laser printer, for example, then it is preferred to store only a single threshold array that comprises unadjusted data. It is preferred to generate the appropriate adjusted threshold array for each color and for the particular type of print media that will be printed upon, and this generation preferably will occur at run time after the printer receives a print job from a host computer.

The adjusted threshold array for each color type/print media type combination used in a particular print job preferably will be generated or derived from one or more parameterized “transfer function equations” that are stored in the printer's non-volatile memory. The non-volatile memory that stores the transfer function equations can either be ROM (such as ROM 16 on FIG. 1), or it can be non-volatile Random Access Memory (also known as NVRAM), such as the NVRAM circuit 26 on FIG. 1. As described hereinabove, the present technology for NVRAM circuits typically uses an EEPROM integrated circuit technology. The use of NVRAM type circuitry makes it possible to easily change the transfer function equations, if desirable. This can be a significant advantage for printers that can be upgraded to use different colors of ink, or different types of print media, which were not part of the original printer design when first manufactured.

The derivation of the transfer function equations preferably is performed by a close inspection of the printer's actual response for a given printed color and a given type of print media. The example provided on FIG. 2 depicts the color magenta that is printed on a sheet of plain paper, as noted above. It is unlikely that a single equation will sufficiently match up to the printer's actual response curve 102 (on FIG. 2), and it is far more likely that more than one such transfer function equation will need to be defined to cover the entire range of gray levels (along the X-axis as seen on FIG. 2). As discussed above, the maximum L* value at a gray level of zero is 94.8 in the example of FIG. 2, and the minimum L* value is 46.1 at the maximum gray level of 255. The following example assumes that the Y-axis (L*) is a function of “x,” which will also be referred to as “f(x),” where “x” is equal to the gray level in the range of 0–255.

In the example of FIG. 2, three different equations were derived to find a “fit” with respect to the actual response curve 102. The first equation is designated by the reference numeral 92, and closely matches the actual response curve 102 in the gray level range from zero (0) through one hundred (100). The second equation closely fits the actual response curve 102 in the gray level range from one hundred (100) through one hundred sixty (160), and is indicated by the reference numeral 94 on FIG. 2. The third equation is designated by the reference numeral 96 on FIG. 2, and closely matches the actual response curve 102 in the range of gray levels from one hundred sixty (160) through two hundred fifty-five (255).

In this example, the first equation (i.e., curve 92) is a quartic equation, as follows: f(x)=94.8269−0.595525x−0.000255349x ²+5.62084·10⁻⁵ x ³−3.19718·10⁻⁷ x ⁴.

The second equation (i.e., curve 94) is a cubic equation, as follows: f(x)=93.8434−0.598143x+0.00276929x ²−4.62357·10⁻⁶ x ³.

The third equation (i.e., curve 96) is also a quartic equation, as follows: f(x)=−149.52+4.0956x−0.0307397x ²+0.000100148x ³−1.20741·10⁻⁷ x ⁴.

While these equations may seem complicated, the amount of memory needed to store these parameterized values in the computer's ROM or NVRAM will be very minimal, especially as compared to the amount of memory space required to hold an entire adjusted threshold array used in halftoning. In the present invention, the typical amount of memory to store a set of transfer function equations ranges between 30 and 70 bytes. Since these transfer functions equations occupy such little space in memory, it makes them imminently feasible for storage in the NVRAM-type of memory, for easy modification (as discussed above).

The number of distinct intensity levels that can be provided by the methodology of the present invention can be made equivalent to that of storing the complete set of adjusted (or corrected) threshold arrays in the printer through the use of the appropriate transfer function equations, and by increasing the bit size of the unadjusted threshold arrays that provide the original data against which the transfer function equations are applied. One important characteristic of the present invention is that the parameterized transfer functions remain the same size, independent of the size of the unadjusted threshold arrays. This offers a distinct advantage over the prior art method of “array mapping” which produces array maps that increase in size proportional to the size of the unadjusted arrays. In the present invention, the parameterized transfer function is simply sampled more frequently for larger unadjusted threshold arrays. The memory storage space required by the methodology of the present invention is less than both the prior art method of “array mapping” and the prior art method of “complete storage,” and the accuracy obtained can be made as good as that of the complete storage methodology.

As discussed above, the methodology of the present invention is very flexible in that the parameterized transfer functions (in the form of the transfer function equations) can be stored in NVRAM since they are very small in size with respect to memory storage requirements. These transfer function equations can be changed very easily, for example, by sending a simple PostScript file to the printer. If a customer needs a different adjusted threshold array, that customer can be supplied with the necessary PostScript file to effect the change. If during development at the factory, for example, new adjusted threshold arrays need to be quickly tested, the transfer function equations can also be conveniently and quickly changed, allowing for efficient testing of the new adjusted threshold arrays.

In addition to the above flexibility, the methodology of the present invention can also allow a user to adjust contrast and brightness quite easily, since rigorous experimentation with various adjustments to unadjusted threshold arrays is feasible by use of this invention. Moreover, the parameterization of the transfer functions tends to hide measurement errors in the original lightness readings. Linearization by itself often does not provide the optimal number of visually unique intensity levels, since a linear increase in dots per level typically does not produce the desired linear L* space. By use of the present invention, it is easy to correct the adjusted threshold arrays to obtain a wider range of dark shades, or a smaller range of light shades, or whatever type of change is needed to gain the best visual spacing of intensity levels by mapping the intensity levels to a curve other than the linear curve, if desirable.

One alternative methodology that uses the principles of the present invention is to intentionally create a non-linear printer response, rather than the typically-desired linear response that substantially matches the human visual perception in L* space. In this alternative method, the printer is provided with transfer functions that, for example, cause the printer to produce an output that emulates some other printer, such as an existing printer that has been previously used to a large extent by a customer for certain reports. When the existing printer is replaced (or supplemented) by a new printer that is capable of producing a substantially linear visual response, the reports may suddenly look “wrong,” because the previously-used existing printer itself did not have a true linear response. The previous non-linear response may have been caused by design, so that certain reports (or photographs, or other contone images, for example) would have a certain distinctive appearance. The “new” printer would need to also produce a non-linear response to make those same reports have the same distinctive appearance. In this situation, the transfer functions would take the non-linear unadjusted threshold array (for each color, where multi-color reports are to be printed), and effectively create an adjusted threshold array that will cause the “new” printer (i.e., printer 10) to create a printed output response that substantially looks like the printed output response of the existing “old” printer which has now been replaced (or supplemented) in a customer's system.

Another example where a non-linear printer response is desirable is to provide a printed output that is appropriate for particular circumstances as an input to a scanning-type apparatus. Examples of such scanning devices include a fax machine, copier, or digitizing scanner. Such scanning devices in certain instances may be better served by having a particular non-linear image for their input, which can be provided by the printer of the present invention.

The first step in generating the graphical data as seen on FIGS. 2 and 3 for a particular printer according to the present invention is to initially print 256 sets of small squares for each color on a particular type of print media. This is the first step 150 as seen on the flow chart of FIG. 4. These 256 squares are to be printed so that each square represents one of the 8-bit gray levels between the numeric value 0–255. Of course, other numeric values could be used for the gray scale, either of lesser or greater resolution, but 256 shades has become the industry standard. Once these squares are made available (i.e., printed) for each color that can be produced by the printer, each of the squares is then measured by shining a bright light on the square and by analyzing the response of each square. This occurs at a step 152 on FIG. 4. It is preferred that a spectrophotometer be used as the brightness or color intensity measuring device, and a preferred brand of the spectrophotometer is manufactured by GretagMacbeth.

Naturally, the light source used should emit the entire visible spectrum of electromagnetic energy, and preferably would have a substantially equal output energy level across the entire visible spectrum. If lesser expensive light sources are used, their spectrum should be known (or become determined), so any necessary compensation can be made for a non-linear electromagnetic radiation output.

For most of the colors, it would be preferred to measure L* of each of the 256 squares, although for yellow, it is preferred to measure b*. It is also preferred to perform this printing and measuring operation for each type of print media that would normally be expected to be used in the printer. This would include plain paper, glossy paper, and coated paper, as well as transparency material. For certain types of printers, it would also be possible to use a more stiff cardboard media, such as paperboard or Bristol board material.

As discussed hereinabove, the response for each color and each type of print media will very likely not be a linear ideal target response. Instead, the output response of most printers probably will be much more like one of the curves depicted on FIG. 3. One primary reason for this non-linear response is a phenomenon called “dot gain.” As is understood by those skilled in the art of halftoning, a binary output image consists of an array of dots. Conceptually, each dot is a perfect square that is situated at a given location within the array. However, an actual printed dot is typically circular instead of square, and furthermore is usually larger and spreads past the boundaries of the conceptual square dot. Therefore, when an image is printed, it will usually look darker than expected. This is the result of step 150 when 256 sets of squares are printed for each color (and on each type of print media).

When measuring the light intensity of each square at step 152, the range of samples that have been printed will range from 0% intensity (i.e., solid black, or solid magenta as the case may be) to 100% intensity (i.e., solid white). When the actual intensity of these samples is measured, the actual intensity will usually be darker than the requested intensity. The inverse of these measurements defines a transfer function which can be used to characterize the dot gain. The transfer function can be used to map the requested tone level (i.e., the gray scale level) to a different—usually lighter—tone level. This level, when printed with dot gain, will produce a tone level that matches the originally requested level. In this manner, the transfer function can compensate for dot gain.

In the present invention, a threshold array is provided as a fast method to halftone an image. Conceptually, a threshold array comprises a two-dimensional array of thresholds, where each threshold is a numeric value. The threshold array is preferably repeated periodically in a tiling manner to fill an arbitrarily large area (e.g., the page to be printed in the form of a bitmap). If the tiled region is, for example, 1024×1024 number of bits or dots, then a large number of copies of a smaller threshold array would be required to cover this 1024×1024 region such that a 16×16 threshold array (for example) would require 64×64 copies (i.e., 4,096 copies). To render a continuous tone input image, each image pixel is compared to the corresponding threshold at the same location. If the image pixel's value is greater than or equal to the threshold value, then a dot will be placed at the corresponding location within the bitmap. Otherwise, no dot will be placed at this location.

In the present invention, it is preferable to provide a stochastic threshold array for each color, at a step 154 on FIG. 4. An exemplary stochastic threshold array can be developed using the principles of U.S. Pat. No. 5,696,602, Ser. No. 08/522,010, filed on Aug. 31, 1995, titled “Method for Halftoning Using Stochastic Dithering with Minimum Density Variance,” which is commonly assigned to Lexmark International, Inc., and is hereby incorporated by reference in its entirety. It is preferred to use a different stochastic threshold array for each color; however, it would be possible to use a single stochastic threshold array for all of the colors, although the results would likely not be as pleasing to the human eye.

When compensating for dot gain, two obvious solutions include using a transfer function to adjust the input pixel values, or to use a transfer function to adjust the threshold values. On one hand, if the input pixel values are adjusted, then every pixel that will ever be printed must be adjusted. On the other hand, if threshold values are adjusted a single time before using the threshold array, then the adjusted threshold array may be used to render images without affecting the pixel values of the incoming images. Therefore, it is preferred to perform dot gain adjustment by applying the transfer function to the threshold array itself.

In the present invention, the transfer function comprises one or more equations that fit the printer's response curve for a particular color and print media combination. An example of such a printer response curve is curve 102 on FIG. 2. Once the one or more equations are determined, they are stored in the printer's non-volatile memory system, such as in ROM 16. Alternatively, the equations could be stored in a type of non-volatile memory that could be easily changed, for example, by a user or by installation of a new printer driver, such as the NVRAM circuit 26 on FIG. 2. The advantages of using an NVRAM circuit to store the transfer functions equations are that, as improvements are made to printer drivers for a given model of printer to use a special color of ink or toner or to print upon a special type of print media, or as the printer ages and its characteristics may change over time, the equations could be changed to match up to the printer's true response curve for a particular combination of color and print media.

In the present invention, the transfer function is applied by using a “parameterized transfer function” (i.e., one or more “transfer function equations”) to convert the unadjusted threshold data into adjusted threshold data for each color. This occurs at a step 156 on FIG. 4. Moreover, it is preferred to use more precise data in the unadjusted array, such as 10-bit data, and then convert this higher precision data to an 8-bit data byte value for each of the numeric values that are entered into the various locations of the threshold array. Obviously, any size binary number could be used for the threshold data elements, however, 8-bit data is not only typical for microprocessor-based systems and standard memory elements (such as Random Access Memory), but further, there is no need for greater precision with respect to the actual human perceptual levels that can be realistically perceived by the average human being. In general, the human eye can see a perceptual difference of approximately 100 different shades of a given color, and when using 8-bit precision, there are a possible 256 different levels of color intensity or shade that can be reproduced. This is much more than is necessary to create a smooth perceptual transition that can be seen or observed by the human eye.

It will be understood that the 10-bit data that is provided in the stochastic threshold array of step 154 could also be of greater precision, merely by using more bits of data to represent each numeric value in the threshold array. However, excellent results have been produced using 10-bit data, and this should be sufficient for most applications. Of course, a stochastic threshold array using 9-bit data would also provide more precision using the principles of the present invention, at least as compared to a stochastic threshold array that would only have 8-bit data numeric values. The overall beneficial effects of using this 10-bit data for the original stochastic threshold array for each color will be discussed in greater detail hereinbelow.

Once the transfer function equations have been generated for each color, it is a simple matter to derive an adjusted 8-bit threshold array for each color that is to be used in halftoning, as at a step 158 on FIG. 4. To perform this operation, the initial stochastic threshold array from step 154 is stored in the Read Only Memory portion of the printer, for example, the ROM 16 from FIG. 1. This typically would be under the control of the graphics engine function 30, which as an executable computer program is also stored in ROM. The transfer function equations themselves would also be stored in ROM 16.

During run time, when it is time to print an incoming print job, the transfer function equations are applied to the stochastic threshold array to create the adjusted 8-bit threshold array in RAM 15 of the printer. When run time occurs, the printer will know what type of print media is going to be used, with the default being plain paper. That being the case, the printer will only require four different adjusted threshold arrays, one per ordinary color that is to be printed (i.e., cyan, magenta, yellow, and black). Therefore, in most cases only four different adjusted threshold arrays having 8-bit element values need be generated using the transfer function equations, then stored in RAM. This is a great memory savings in comparison to the prior art printers that had to store the entire set of adjusted threshold arrays for all combinations of colors and types of print media in the ROM of their printer's memories.

It will be understood that the adjusted 8-bit threshold array need not be stored in true random access memory for the invention to be operative. Instead, any sufficiently numerous group of registers could be used instead of RAM, including registers that reside within an ASIC (Application Specific Integrated Circuit). Since ASICs are constantly being made more flexible and more powerful (i.e., with greater numbers of programmable elements), it may be preferred at some time in the future to use ASIC registers of ASIC 20 to hold the adjusted threshold arrays utilized by the present invention.

A nuance of FIG. 4 not previously discussed is the use of data “packing” and “unpacking,” in which the data values for the stochastic threshold arrays are packed into as tight as possible memory locations in the printer's ROM. In many microprocessor-based systems, 10-bit numeric values would each require a 16-bit data word for memory storage. By packing the data according to the step 170 on FIG. 4, the printer can save over 35% of the memory storage space that would normally be used to contain this same amount of data. Of course, the data while in its packed state is less useful and harder to get at, so it is preferred to first unpack that data at a step 180 on FIG. 4 before attempting to use the data at run time. The details of packing and unpacking data are provided in other flow charts, as discussed hereinbelow.

In a preferred system, the printing and measuring steps 150 and 152 are performed “off-line” at the factory, and the stochastic threshold array at step 154 is also provided at the factory. Furthermore, the transfer function equations of step 156 preferably are also derived at the factory based upon the dot gain data from the light measuring step 152. It is preferred that the stochastic threshold array elements have their data or numeric values stored in a packed format, as per the step 170, at the factory and stored in the printer's ROM 16.

In the preferred printer, at run time the processing circuit of the printer merely needs to unpack the data at step 180, and then derive the adjusted 8-bit threshold arrays for the colors that are going to be used for a particular type of print media, as per step 158. While this will take a small amount of time, this processing time will be mainly indiscernible to the human user when added to the amount of processing time required to otherwise prepare the printer at run time for each new incoming print job.

The packing step 170 of FIG. 4 is depicted in greater detail in a flow chart on FIG. 5. Starting at a step 200, some variables are set to initialized values, including a variable “bit_buffer_size” that is set to 32, and a variable “bits_requested” is set to the value 10. At a step 202, a variable “bit_buffer” is set to 0, and a variable “bits_in_buffer” is also set to 0.

By use of these initial variable values, it is assumed that the array elements are 10-bit values, although different element sizes could be used merely by changing the size of the “bits-requested” variable. At the same time, the “bit_buffer_size” variable is microprocessor dependent, and should be set to the most efficient data size for the microprocessor that will be used to pack and unpack the data. Today, many microprocessors contain 32-bit wide registers.

The main input for this packing routine 170 is a two-dimensional 10-bit threshold array (stored in 16 bits), named “inarray[r][c],” in which the variable “r” refers to the element at row “r” and the variable “c” refers to the element at column “c” of this array. The output of this routine 170 is a one-dimensional stream of data containing the packed contents of the input array.

At a step 204, the “row” variable “r” is set to its initial value of zero (0). At a decision step 206, the value of “r” is compared to see if it is less than the numeric value of a variable named “rows” that, in the preferred embodiment, is set equal to the number 128. The value for a variable called “cols” is also preferably set to 128, since the preferred stochastic threshold array has a size that is 128×128 rows and columns.

The value for the variable “r” will be incremented throughout this routine 170, and initially the result at the decision step 206 will always be YES until the routine has incremented the value for “r” up to the number 128. During the first pass, the logic flow is directed to a decision step 208 that asks a similar question regarding the value for “c” with respect to the numeric value of the variable “cols.” Again, the initial passes will always result in a YES answer, thereby directing the logic flow to a step 210.

At step 210, the variable “bits_in_buffer” is set equal to itself plus the value of the variable “bits_requested.” Since the value of the variable “bits_requested” was set to ten (10), this step 210 will always result in a new value for the variable “bits_in_buffer” being increased by the amount of ten.

A decision step 212 now determines whether or not the variable “bits_in_buffer” is greater than or equal to the variable “bit_buffer_size.” With the values set for the “bit_buffer_size” of thirty-two and the “bits_requested” value of ten, the first three passes into this decision step 212 will result in a NO answer, thereby directing logic flow to a step 214. At step 214, the variable “bit_buffer” is set equal to a numeric value that is equal to the variable “inarray[r][c]” that is logically OR'ed to the current value of the variable “bit_buffer” that is shifted left by the number of bits that is currently the numeric value of the variable “bits_requested.” After this occurs, the logic flow is directed to a step 216 where the value for the variable “c” is incremented by one.

The logic flow now reaches a point on the flow chart of FIG. 5 referred to as 222, and is designated “A,” which directs the logic flow back to a point 224 on FIG. 5, in which the next operation is the decision step 208. Until all of the columns in the array have been completed, the answer will again be YES at decision step 208, and the logic flow is directed to the step 210. After that occurs, the decision step 212 is reached, and for the next two passes, the step 214 is reached that affects the value of the variable “bit_buffer.” Each time that occurs, the value of “c” is incremented at step 216, and the logic flow is directed back to the decision step 208 via the letter “A.”

The fourth time that decision step 212 is reached in this example, the result will be YES, and a step 220 will be reached. In step 220, the variable “bits_in_buffer” is set equal to itself minus the variable “bit_buffer_size” (which has a value of 32). Next a variable called “outbits” is set equal to a rather complex mathematical value. “Outbits” is the one-dimensional stream of data that is the output of this packing routine 170. In step 220, “outbits” is set equal to the variable “bit_buffer” after it has been shifted left by the number of bits equal to the quantity (“bits_requested” minus “bits_in_buffer”), and this value is logically OR'ed to the quantity “inarray[r][c]” that is shifted right by the number of bits equal to the value of the variable “bits_in_buffer.”

After this occurs, the number of bits equal to the variable “bits_in_buffer” is written from the variable “outbits” to the packed array in memory. The variable “bit_buffer” is now set equal to the current element of “inarray[r][c],” which is the last function that occurs within step 220. After that occurs, the variable “c” is incremented at step 216, and the logic flow is directed back via “A” to the decision step 208.

Eventually, all of the 128 columns will have been filled for the first row of the array, and the result at decision step 208 will become NO. When that occurs, a step 230 sets the value of “c” back to zero (0), and the value of “r” is incremented by one. After that occurs, the logic flow is directed back to decision step 206 that determines if the value of “r” is less than the variable rows, which will not occur until all of the rows of the array have been operated upon. When only the second row of the array has been reached, the logic flow is directed back through the YES result to the decision step 208, where the columns begin to be operated upon again.

When the logic flow has finally reached the final row, the result at decision step 206 will become NO, and the logic flow will be directed to a decision step 232. At this decision step, it is determined if the variable “bits_in_buffer” is greater than zero (0), and if the answer is NO, then this routine is finished at the step 236. However, in the general case, there will be some left over bits that need to be handled, and the result at decision step 232 will likely be YES. In that circumstance, a step 234 sets the variable “outbits” equal to the value of the variable “bit_buffer” after it is shifted left by the number of bits equal to the quantity “bit_buffer_size” minus “bits_in_buffer.” Once that has been accomplished, the logic flow reaches the return step called “done” at 236, and the packing routine 170 is finally completed.

While data compression could be applied to reduce the amount of memory, it is preferred to use the packing routine as illustrated on FIG. 5 to pack or “squeeze” the numeric elements together within the printer's memory. The unused bits of each 16-bit word are eliminated, so that a single 10-bit element immediately follows the previous 10-bit element. This makes the individual elements more difficult to access later, and an unpacking routine preferably will be used to first re-arrange these 10-bit elements into a more easily addressable set of values in the printer's memory.

In the example of FIG. 5, it was assumed that ten bits per element was needed, while of course, other element sizes could be used instead. Moreover, a variable number of bits per element is also possible, although this would involve additional complexity. One method for accommodating a variable number of bits would be to encode the number of bits per element along with the actual data. Another method would be to synchronize the packing and unpacking routines so as to use the proper number of bits for each consecutive element.

Although packing the array data reduces memory space, the individual array elements are more difficult to access when packed. To allow for more convenient access of the array elements at run time, the data may be unpacked. The routine 180 is illustrated in greater detail in the form of a flow chart on FIG. 6. In this unpacking example, it is assumed that each packed element requires ten bits, although other element sizes may be used instead if desirable. Of course, if an array of elements has been packed using “x” number of bits per element, then the unpacking routine 180 must also unpack assuming that there are “x” bits per element. Otherwise, the results will be nonsense.

As an alternative, a variable number of bits per element is possible, although this would involve additional complexity. One method for accommodating a variable number of bits (as noted above) would be to encode the number of bits per element along with the data itself, whereas another method would be to synchronize the packing and unpacking routines so that they use the proper number of bits for each consecutive element.

In the unpacking routine 180, the input information is a one-dimensional stream of data containing the packed contents of the input array. The output of this routine 180 is an uncorrected, two-dimensional 10-bit threshold array, named “outarray” in this example. The notation “outarray[r][c]” refers to the element at row “r” and column “c” of this array.

The routine starts with a step 250 in which a variable named “bit_buffer_size” is set to the value of 32, which is a convenient standard size of a single element for a microprocessor that utilizes 32-bit registers. Also in step 250, a variable named “bits_requested” is set to the value of ten (10) which, as stated before, means that there are ten bits per array element in the packed data.

Next a step 252 places the value of the variable “bit_buffer_size” into a variable named “bits_in_buffer.” This step then reads the next number of bits equal to the value of the “bits_in_buffer” variable from the packed array into a variable named “bit_buffer.”

Now that the main working variables have been initialized, a step 254 sets a variable “r” equal to zero, (0), after which a decision step 256 determines whether the value of “r” is less than the value of a variable named “rows” which is set to the value 128, since the preferred array size is 128×128 number of elements in rows and columns. Of course, a different size array could be used, in which case the value for the variable rows would be set to a different number. At this first pass, the result of this decision step 256 will be YES, and the logic flow is directed to another decision step 258.

At decision block 258 the value of the variable “c” is compared to see if it is less than the value of a variable “cols” which represents the number of columns in the array. In this example, the value of the variable “cols” is set to 128. At this first pass, the result will be YES at decision step 258, and the logic flow is directed to a step 260.

At step 260, the variable “unpacked[r][c]” is set equal to the value in the variable “bit_buffer” after it has been shifted right by the number of bits equal to the quantity “bit_buffer_size” minus “bits_requested.” After this occurs, the “bits_in_buffer” variable is set equal to itself minus the value of the variable “bits_requested.”

A decision step 262 now determines whether or not the variable “bits_in_buffer” is less than zero (0). In this example, the first three passes through decision step 262 will result in a NO answer to this comparison, since the “bit_buffer_size” variable was set to 32 and the size of the data elements is 10 bits. In view of this NO result, the logic flow is directed to a step 264 which places in the variable “bit_buffer” the value of itself after it has been shifted left by the number of bits that equals the numeric value currently in the variable “bits_requested.”

After this has occurred, a step 266 increments the value of “c,” which means that it is time to move to the next column of data in the array. After that has occurred, the logic flow is directed back to decision step 258, where it is determined whether or not the value of “c” is still less than the value of “cols” (which is set to the value 128). At this second pass through decision step 258, the result will be YES, and step 260 is again executed. This will occur for the first 128 passes through this portion of the flow chart of FIG. 6. Once the logic flow arrives at decision step 262 after the first three passes, the result will become YES upon the fourth pass through this decision step 262. When that occurs, a step 270 will perform several functions.

At step 270, a certain number of bits will be read from the packed array and placed into the variable “bit_buffer.” This number of bits is equal to the variable “bit_buffer_size,” which in this example is equal to 32 bits. After that occurs, the variable “bits_in_buffer” is set equal to itself plus the value of the variable “bit_buffer_size.” After that occurs, the output array variable “unpacked[r][c]” is set equal to itself (at this same row and column position) which is logically OR'ed with the value of the variable “bit_buffer” after it has been shifted right by the number of bits that equal the current numeric value of the variable “bits_in_buffer.” The variable “bit_buffer” is now set equal to itself after it has been shifted left by the number of bits that equals the quantity “bit_buffer_size” minus “bits_in_buffer.”

The value of “c” is now incremented at step 266 and the logic flow is directed back to the decision step 258 for further passes at different columns of the array in this first row. Once all of the columns have been processed, the variable “c” will ultimately reach a value of 128, and at decision step 258 the result will finally become NO. When that occurs, a decision step 280 resets the value of “c” back to zero (0), and the value of the row variable “r” is incremented. After that occurs, decision step 256 is arrived at, which compares the current value of “r” to see if it is less than the value of the variable “rows” (which was earlier set to 128).

For each new value of “r,” all of the columns of the array are processed, basically using an internal DO-loop, and then the value of the row variable “r” is incremented. After all of the columns have been processed for all of the rows, the value of the variable “r” will finally reach 128 at step 280, and decision step 256 will finally have a result equal to NO. When that occurs, this routine 180 is finished and can return, at a step 282 referred to as “Done.”

The end result of routine 180 is to provide an unadjusted 10-bit element size stochastic threshold array having 128 rows and 128 columns. The resulting unadjusted array is unpacked, which means that each 10-bit element is placed in a separate two-byte memory location within the RAM 15 of printer 10, at run time. The transfer function equations can now be easily applied to the unadjusted threshold array at this point, in the form of temporarily-stored look-up tables that contain conversion data. These look-up tables are preferably stored in the printer's RAM 15 at run time, and these look-up tables are generated by application of the transfer function equations for a specific combination of color and type of print media.

In a sense, the above look-up tables do not in the least depend upon the preferred unadjusted stochastic threshold arrays; the only important criteria are the data precision of the unadjusted threshold array elements (e.g., 10-bit data in the range of 0–1023) and the actual size in rows and columns of the unadjusted threshold array (e.g., a 128×128 array). The values in the temporary look-up tables are applied to the unadjusted threshold array using a routine 158 that is depicted in the form of a flow chart on FIG. 7. Once the adjusted threshold array is fully developed by application of the functions in the flow chart of FIG. 7, the temporary look-up table may be abandoned, and its space in RAM can then be re-allocated for other printer uses, such as deriving a second adjusted array of a different color/print media combination for the very same print job.

The input to this routine 158 is the unpacked uncorrected threshold array having 10-bit elements that are arranged in two-byte memory locations. The output of this routine is an adjusted (or corrected) threshold array that has elements of 8-bit size, in which each 8-bit element is placed in a single 8-bit byte in the printer's RAM. This all occurs at run time when the printer needs to process an incoming print job.

On FIG. 7 starting at a step 300, the row variable “r” is set equal to zero (0). A decision step 302 then determines whether the current value of “r” is less than the variable named “rows,” which in this example, is set equal to the value of 128 (since there are 128 rows in the threshold array). Naturally, at this first pass the result will be YES at decision step 302.

A decision step 304 now determines whether or not the variable “c” is less than the value for a variable “cols,” which is set equal to 128 (since there are 128 columns in the threshold array). Of course, at this first pass the result will be YES, and the logic flow is directed to a step 306. At step 306, a variable named “corrected_thresh_array[r][c]” is set equal to the look-up table result, which is a variable named “xfer[unpacked[r][c]].” This “xfer” variable comprises a look-up table, an example of which is provided in TABLE #5, hereinbelow. In more detail, the variable called “unpacked[r][c]” comprises an unadjusted threshold array, an example of which is provided in TABLE #4 (i.e., for a 32×32 threshold array example). The look-up table provided in TABLE #5 is also a 32×32 array, and is an example of the look-up table that would be used in the step 306. The output adjusted (or corrected) threshold array that is calculated at step 306 preferably is a 128×128 sized array, and an example of such 8-bit adjusted array (as a 32×32 sized array) is provided in TABLE #6, hereinbelow. These example tables provided below will be discussed in greater detail. It will be understood that the preferred size of all the arrays being described herein is 128×128, although any size could be used without departing from the principles of the present invention. The example arrays provided in the TABLES #1–6 herein are of a smaller 32×32 size only for the purposes of illustration.

The unpacking routine 180 and the transfer function equations (using the temporary look-up tables) application routine 158 preferably are always executed at run time within the printer 10. It should be noted that, from a processing time standpoint, it will likely be much more efficient to both unpack the 10-bit data that makes up the unadjusted threshold array and then apply the transfer function equations (again, using the temporary look-up tables) to that particular row and column of the unadjusted array to create the corresponding adjusted 8-bit array element, all in a single operation. By doing so, one can eliminate the middle step of generating an unpacked 10-bit unadjusted array in RAM in two-byte increments, and instead generate the final 8-bit unadjusted array in elements of RAM that are single byte elements, meaning that (of course) the 8-bit array elements are completely packed within 8-bit bytes of memory locations in RAM. Not only is processing time saved, but also temporary memory allocation space is saved. Such a combined unpacking and transfer function equations application routine with look-up tables is described in a flow chart depicted on FIG. 8.

On FIG. 8, a first step 350 initializes two of the variables that were also seen on earlier flow charts on FIGS. 5 and 6. These variables are the “bit_buffer_size,” which is set to a value of 32, and the variable “bits_requested” which is set to a value of ten. The next step is to place the value of the variable “bit_buffer_size” into a variable called “bits_in_buffer,” after which a certain number of bits are read from the packed array and placed into a variable called “bit_buffer.” The number of bits to be read in is equal to the value of the variable “bits_in_buffer.”

The logic flow now arrives at the point where the row and column data is operated on, starting with a step 354 that sets the row variable “r” to zero (0). After that occurs, a decision step 356 determines whether or not the current value of “r” is less than the value of a variable “rows” that was set to 128 in the preferred embodiment, since a threshold array having 128 rows and 128 columns is used.

During this first pass, the result at decision step 356 will be YES, and next a decision step 358 determines whether or not the current value of a variable “c” is less than the value of a variable “cols,” which also has a value of 128 since the preferred embodiment uses a threshold array that has 128 columns. At this first pass, the result at decision step 358 will be YES, thereby directing the logic flow to a step 360.

In step 360, a variable “unpacked_val” is set equal to the “bit_buffer” variable after it has been shifted right by the number of bits equal to the quantity “bit_buffer_size” minus “bits_requested.” The current array element of the output of this combined routine, which is a variable named “corrected_thresh_array[r][c],” is now set equal to the transfer function of the unpacked value, which in this example has the name “xfer[unpacked_val].” As before in the flow chart of FIG. 7, the example 10-bit to 8-bit look-up table provided in TABLE #5 hereinbelow is exemplary for the transfer function referred to as “xfer” at step 360, i.e., for a 32×32 array (rather than the preferred 128×128 array). Furthermore, the packed data represented by the variable “unpacked_val” is represented as a 32×32 example on TABLE #4 hereinbelow, while the adjusted 8-bit threshold array having the variable name “corrected_thresh_array” is also represented in a 32×32 size array example in TABLE #6, hereinbelow.

The last operation at step 360 is to calculate a new value for the “bits_in_buffer” variable, which is set equal to itself minus the value of the variable “bits_requested.” The logic flow now arrives at a decision step 362, where this “bits_in_buffer” is compared to see if it is less than zero (0). For the first three passes through this flow chart of FIG. 8, the result will be NO, and the logic flow will be directed to a step 364.

At step 364, the variable “bit_buffer” is set equal to itself after it has been shifted left by the number of bits of the value of the “bits_requested” variable. After that occurs, the column is changed by incrementing the variable “c” by one, at a step 366.

The logic flow is now directed back to decision step 358, where the value for c is compared to see if it is less than the value of the variable “cols” (which was earlier set to 128). Since the answer will be YES at this next, second pass, the step 360 will be executed, as well as the decision step 362, ultimately leading to the step 364. This loop will remain intact until the fourth pass through, at which time the result at decision step 362 will change from NO to YES. When that occurs, the logic flow is directed to a step 370.

At step 370, many of the same functions are performed as were executed in the step 270 depicted on FIG. 6. For example, the packed array is inspected and the next pre-determined number of bits are placed into the variable “bit_buffer.” This number of bits is equal to the value of the variable “bit_buffer_size,” which in this example is set to the value of 32. After that occurs, the variable “bits_in_buffer” is set equal to itself plus the value of the variable “bit_buffer_size” (which is equal to 32) A new variable referred to as “temp” is now set to the value of the “bit_buffer” variable after that variable has been shifted right by the number of bits equal to the current value of the “bits_in_buffer” variable.

At this time, the appropriate row and column element of the unpacked array, having the variable name “unpacked[r][c],” is set equal to itself after it has been logically OR'ed to the variable “temp.” Finally, the variable “bit_buffer” is set equal to itself after it has been shifted left by the quantity “bit_buffer_size” minus “bits_in_buffer.” After this occurs, the column element is changed by incrementing the variable “c” at step 366.

This internal “DO-loop” is performed until all 128 columns have been processed, and when that finally occurs, the result at decision step 358 will change from YES to NO. When that occurs, a step 380 will reset the variable “c” back to zero (0), and will change the row position by incrementing the variable “r.” The logic flow is now directed back to the decision step 356 to determine if the value of “r” is now less than the value of “rows” (which is equal to 128). If the logic flow has just arrived to the second row position, then the result at decision step 356 will, of course, be YES, and the logic flow re-enters the internal DO-loop that operates upon the various columns of this array.

When all columns and all rows have finally been processed, the logic flow will leave the step 366 and arrive at the decision step 358, which will then flow to the step 380, thereby incrementing the value of “r” to the point where the result at decision step 356 will be NO. When this occurs, this combined routine will be finished and can return, which is depicted as the step 382 as being “Done.”

It is now appropriate to discuss the various tables that are included below, which will help to emphasize the advantages of the present invention. TABLES #1–3 are exemplary of a non-preferred methodology that takes an unadjusted 8-bit stochastic threshold array and converts it to an adjusted 8-bit threshold array.

TABLE #1 depicts a 32×32 stochastic threshold array that comprises 8-bit values for its individual array elements. There are 256 total possible values for the 8-bit array elements, and there are 1024 possible array locations on this 32×32 array. Since the array is unadjusted, there should be four elements of each value somewhere within this stochastic threshold array. Since it is based on an ideal “machine” response, it is unlikely to lead to a linear perceptual result with respect to the lightness versus darkness of each individual incremental change as perceived by the, human eye. In other words, this would likely lead to a graph such as the response curve 102 on FIG. 2, which exemplified a magenta color set of data on plain paper.

TABLE #2 represents a look-up table that is used to convert the unadjusted 8-bit values to adjusted 8-bit values. Since there are only 256 possible values (ranging from the values 0–255), this look-up table is a much smaller array, being 16×16, thereby providing 256 possible values. It should be noted that the value zero (0) will not actually be found on the threshold array in this example, so in actuality only 255 possible values will be converted (ranging from 1–255).

TABLE #3 is the adjusted 8-bit array that is derived by using the look-up table of TABLE #2 to convert the unadjusted values of TABLE #1. TABLE #3 has a size of 32×32, which provides a total of 1024 possible element locations. Since this example uses 8-bit precision, there will be a minimum of four elements of any given value somewhere on the rows and columns of this adjusted array. However, it will be understood that some numeric values will have many more than four element locations (since this array is adjusted). At the same time, it will also be understood that some numeric values will not be in the adjusted array of TABLE #3 at all. Such values can be easily found by inspecting TABLE #2. For example, in the top row of TABLE #2, the positions zero (0) through fifteen (15) show values as follows: 0, 1, 4, 7, 10, 13, 17, 20, 23, 26, 29, 32, 35, 38, 41, and 44. All of the numbers missing between those numbers listed in the previous sentence are numeric values that will not appear anywhere on TABLE #3. For example, the numeric values skip from 1 to 4, which means there will be no elements having numeric values for either 2 or 3 in TABLE #3.

TABLE #1 8 bit Unadjusted 32 × 32 Threshold Array 230 71 141 242 30 214 40 199 59 219 113 12 161 49 135 185 31 129 189 17 163 57 142 109 158 14 170 251 57 215 15 31 101 215 48 119 227 97 249 14 211 125 51 102 179 30 195 152 159 75 138 196 26 155 34 185 58 150 231 130 24 238 57 112 222 12 252 36 129 220 45 113 239 38 7 192 156 42 127 208 133 108 159 54 178 5 197 145 30 167 217 35 50 224 151 77 18 232 25 111 73 244 132 52 207 117 39 139 198 98 3 241 165 54 181 121 154 17 96 184 16 252 104 227 25 129 190 52 111 206 93 115 230 115 214 70 162 55 172 153 146 248 75 173 150 33 246 146 51 169 22 240 125 202 5 183 115 40 205 20 73 137 51 206 208 30 191 109 32 92 220 72 234 95 153 131 225 20 135 235 2 179 58 152 128 118 49 156 10 189 34 211 167 37 195 45 157 112 254 14 33 195 101 246 125 52 225 111 17 249 126 79 223 29 122 203 134 25 157 40 201 163 97 1 119 160 14 205 141 91 181 41 237 75 215 120 81 24 250 176 233 57 179 107 47 243 53 171 98 186 12 148 223 127 54 133 30 207 46 229 137 5 214 129 23 140 230 39 36 166 204 91 134 97 157 33 190 102 151 58 251 11 45 175 242 104 13 221 199 20 247 130 32 233 29 196 55 211 157 74 21 197 152 75 36 173 78 215 9 125 177 92 170 3 106 217 142 36 51 255 219 114 46 168 110 204 44 239 76 144 247 18 113 232 174 27 58 238 139 10 254 70 154 20 138 53 94 171 201 5 102 146 151 3 193 123 57 190 100 222 35 207 136 29 71 161 232 81 105 177 30 228 148 7 166 47 178 13 225 116 244 130 33 237 250 55 203 25 107 210 52 235 111 51 77 184 18 86 196 112 13 152 51 143 242 72 175 120 27 253 49 105 220 165 54 143 172 39 233 121 39 191 15 144 212 38 189 117 36 120 250 23 56 215 5 186 33 136 247 83 44 171 40 240 96 199 76 153 145 110 158 78 224 32 103 217 157 73 202 51 174 8 182 55 227 44 255 23 149 118 194 10 126 234 38 142 114 235 50 219 37 156 39 198 59 237 70 181 55 146 100 226 26 150 35 167 8 208 36 115 176 2 165 92 245 22 187 82 204 107 245 31 96 2 205 124 44 225 7 129 222 27 247 55 135 130 106 51 231 154 57 174 38 41 199 51 156 89 125 192 18 34 202 149 16 129 221 24 249 37 115 240 52 197 8 145 213 122 4 243 254 37 51 183 138 103 176 22 168 75 231 91 28 236 136 46 10 155 200 96 5 214 59 224 119 206 19 133 188 58 179 30 180 109 31 229 154 58 136 94 15 151 106 253 59 152 21 193 54 220 133 57 125 235 41 132 244 71 171 13 217 115 209 31 149 17 168 246 25 100 155 210 14 194 53 182 140 47 97 248 103 209 90 45 142 203 3 32 160 117 238 32 27 229 143 5 236 58 191 114 184 52 251 129 224 1 79 198 114 154 59 200 50 158 11 225 35 121 170 48 95 172 139 42 219 18 238 122 35 253 128 93 139 233 21 150 215 57 243 109 148 31 171 43 183 28 171 56 204 74 195 113 32 192 14 181 35 255 34 132 140 218 28 242 15 159 54 248 141 51 151 77 201 136 8 216 55 117 153 41 138 104 178 11 91 234 100 218 52 105 194 71 236 9 213 123 54 208 79 223 154 39 152 23 161 229 11 147 43 182 50 165 231 18 149 47 118 206 74 246 123 59 180 110 137 108 245 32 131 39 253 101 175 12 109 134 42 210 4 241 187 22 147 134 197 156 30 211 66 240 56 102 177 39 163 53 54 209 39 279 4 73 190 123 159 35 139 223 21 252 66 187 124 159 43 158 117 239 112 17 229 37 183 60 198 108 144 15 222 10 241 53 203 48 182 78 130 216 1 127 156 34 234 124 50 192 119 143 28 150 95 249 43 149 105 243 59 10 76 213 170 98 59 212 103 332 5 128 207 26 193 48 209 9 186 41 3 155 251 29 174 85 202 250 108 157 90 158 82 229 99 134 226 34 46 194 124 31 128 163 227 56 254 19 180 120 35 200 94 185 132 55 218 110 245 30 13 147 52 201 53 148 244 72 220 29 230 147 11 172 40 191 122 221 88 131 237 7 115 185 127 152 43 38 236 60 213 101 172 37 195 29 169 95 221 24 15 248 113 200 74 156 131 17 72 241 118 150 49 206 77 128 121 70 177 19 188 33 252 115 205 93 2 232 104 154 42 191 213 144 56 239 107 153 82 184 46 175 40 79 212 19 250 137

TABLE #2 Transfer Function Table to Convert 8-bit Values to 8 bit Values | *0 *1 *2 *3 *4 *5 *6 *7 *8 *9 *10 *11 *12 *13 *14 *15  (0) 0 1 4 7 10 13 17 20 23 26 29 32 35 38 41 44  (16) 47 50 53 56 59 62 64 67 70 73 75 78 81 84 86 89  (32) 91 94 96 99 101 102 106 108 111 113 115 117 119 121 123 125  (48) 127 129 131 133 135 137 139 140 142 144 146 147 149 150 152 153  (64) 155 156 158 159 160 162 163 164 166 167 168 169 170 172 173 174  (80) 175 176 177 178 179 180 181 183 184 185 186 187 188 189 190 199  (96) 192 194 195 196 197 198 198 199 199 200 201 202 203 204 205 206 (112) 206 207 208 209 210 210 211 212 213 213 214 215 215 216 217 217 (128) 218 219 219 220 220 221 222 222 223 223 224 224 225 225 226 226 (144) 227 227 228 228 229 229 229 230 230 231 231 231 232 232 233 233 (160) 233 234 234 235 235 235 235 236 236 236 236 237 237 237 237 237 (176) 238 238 238 238 239 239 239 240 240 240 240 241 241 241 242 242 (192) 242 242 243 243 243 243 244 244 244 244 245 245 245 245 246 246 (208) 246 246 247 247 247 247 247 248 248 248 248 248 248 249 249 249 (224) 249 249 249 250 250 250 250 250 250 250 251 251 251 251 251 251 (240) 251 252 252 252 252 252 252 253 253 253 253 253 254 254 254 254

TABLE #3 8-bit Adjusted 32 × 32 Threshold Array-From 8-bit Unadjusted Array 250 164 225 252 175 247 111 244 162 248 211 35 234 129 222 240 89 219 241 50 235 244 226 204 233 96 236 253 159 248 47 176 198 248 127 212 250 194 253 41 247 216 133 198 238 186 243 230 236 170 224 243 75 231 179 240 246 229 250 219 70 251 144 206 249 35 254 181 218 248 121 207 251 184 20 242 232 115 217 246 221 203 233 139 238 10 243 227 86 236 248 180 249 249 234 172 106 250 73 247 167 252 220 152 246 210 108 224 244 195 7 252 235 155 239 213 231 104 192 240 47 254 199 250 73 219 242 135 206 246 189 44 250 210 247 163 234 140 237 153 228 253 169 237 229 94 252 228 137 236 64 251 216 254 13 240 209 111 245 59 167 241 150 201 246 175 242 204 91 188 248 166 251 171 231 220 249 59 22 251 4 238 146 230 250 224 129 232 29 241 96 247 236 183 243 121 232 206 254 41 178 243 198 252 217 152 249 206 104 253 217 174 249 84 214 245 222 75 236 111 244 235 194 1 212 233 41 245 225 187 239 113 251 169 248 213 176 70 253 238 250 144 238 202 125 252 153 237 195 240 35 229 249 217 139 221 86 246 158 250 22 17 247 218 67 225 250 185 101 235 245 187 222 194 232 94 242 198 230 160 253 206 121 237 252 199 38 249 244 59 253 219 278 250 81 243 140 247 232 168 62 243 230 169 181 237 173 248 26 216 238 188 236 70 201 248 226 181 133 254 248 208 123 236 205 245 119 251 170 227 253 106 207 250 237 78 146 251 224 86 254 183 231 59 241 237 190 237 244 17 198 228 230 7 242 215 144 242 197 249 180 246 223 84 164 234 247 176 200 238 175 250 229 20 235 125 238 38 249 210 252 219 94 251 253 156 245 73 202 242 152 251 206 230 172 240 253 181 243 206 53 234 133 226 252 166 237 213 78 254 129 200 248 235 139 226 237 185 250 233 108 242 47 227 247 184 241 223 101 213 253 67 142 248 17 240 189 223 253 178 119 237 10 251 192 244 170 231 227 205 233 173 249 91 199 248 232 67 245 150 237 23 239 156 250 119 254 67 229 211 243 29 217 251 106 226 208 251 131 248 183 235 196 244 147 251 163 239 140 228 197 249 75 229 181 236 23 246 101 209 238 4 235 188 252 164 241 177 245 202 252 89 192 4 245 215 119 249 20 219 249 78 253 140 222 239 201 150 250 235 159 237 184 225 244 153 232 196 216 242 106 179 245 229 101 219 249 70 253 104 209 251 253 243 26 227 248 214 10 252 254 83 133 240 224 199 238 64 236 169 250 187 81 251 223 123 29 231 244 192 13 247 162 249 212 246 108 221 241 160 238 186 239 204 89 260 235 146 240 190 14 230 201 254 147 234 62 242 155 248 221 159 217 251 113 220 252 164 237 38 248 210 246 176 229 50 236 256 73 197 231 247 96 243 237 239 225 125 194 253 199 246 186 121 226 245 23 177 233 210 251 188 78 250 226 13 251 160 242 208 240 152 153 218 249 1 174 244 208 235 147 244 131 233 32 249 99 213 236 127 191 238 222 115 248 53 251 214 180 254 218 189 224 250 62 229 248 159 252 204 229 178 237 117 240 81 237 142 245 168 243 207 91 242 41 239 99 254 190 220 225 248 173 252 44 233 139 253 225 150 236 172 244 233 23 248 156 210 231 113 241 119 238 32 187 251 197 248 135 200 243 164 251 26 247 219 155 246 174 249 235 108 230 67 234 250 32 228 117 239 149 235 250 53 227 125 211 246 168 252 215 162 239 205 223 201 252 91 220 185 254 198 234 35 241 222 115 247 10 252 241 64 228 179 243 232 86 247 151 251 142 198 238 185 235 137 155 246 196 249 10 167 242 215 233 99 224 249 62 254 158 241 215 233 117 236 210 251 206 50 250 183 240 149 244 203 207 47 249 29 252 160 245 127 239 173 219 248 1 217 231 96 251 215 131 242 212 216 81 233 191 253 117 229 200 252 162 236 170 147 236 195 147 247 199 250 17 224 246 75 242 127 246 26 24 113 7 231 253 56 237 180 245 131 203 238 186 233 177 250 196 222 249 178 123 243 215 89 218 235 250 158 254 56 239 213 99 244 190 240 220 156 248 205 252 175 38 228 135 244 153 229 252 166 247 84 250 228 32 237 111 242 214 249 184 220 251 20 209 240 217 234 117 195 251 149 247 198 237 104 243 84 236 191 249 70 44 253 207 244 68 235 220 50 166 252 211 233 129 246 172 238 213 163 238 56 241 94 254 210 245 189 1 250 199 231 115 242 247 227 142 251 202 231 177 240 123 237 225 174 247 56 253 223

To provide a specific example of how the look-up table is used, one should inspect the bottom left-hand array element of TABLE #1. As can be seen from this inspection, the numeric value is equal to “8.” Now one is to inspect TABLE #2 for the numeric value 8. This value is found along the top row at the ninth position from the left, and the value found at that position is, the number “23.” In other words, the unadjusted value of 8 is to be adjusted (or corrected) by replacing that “8” with the value “23.” Now one should inspect TABLE #3 at the bottom left-hand array element position, and it will be seen that the numeric value “23” is located at that position.

Since the example of TABLES #1–3 used 8-bit precision throughout, many numeric values are missing from the adjusted output array of TABLE #3. This is particularly true for the lighter shades, since the human eye can perceive more fine differences in shading in the lighter shades than can be produced by the 8-bit resolution of these tables. This phenomenon is more clearly illustrated in the histogram of threshold values provided on FIG. 9. As can be seen, there are many threshold values along the left portion of this chart (along the gray scale axis) that have no numeric values associated. In other words, the number of occurrences within the adjusted 32×32 array is equal to zero (0) for many of the threshold values having values less than one hundred. It may be true that 8-bit adjusted arrays have been derived in the past from 8-bit unadjusted arrays, mainly stemming from operations performed at the factory of printer manufacturers. However, the prior printers typically store those adjusted threshold arrays in the printer's ROM, and since several different arrays are required to compensate for various types of print media and various colors that can be output by a color printer, these corrected or adjusted threshold arrays take a significant amount of memory space in the printer's ROM. One of the primary advantages of the present invention is to minimize the amount of ROM required to store the original unadjusted threshold arrays, as well as the look-up tables. This will be illustrated in an example, hereinbelow.

TABLE #4 10-bit Unadjusted 32 × 32 Threshold Array 924 283 564 972 320 859 156 798 273 877 473 45 644 194 540 743 122 516 759 64 651 225 567 436 633 133 683 1007 268 867 62 321 405 865 192 475 909 386 1000 53 847 499 201 408 719 359 782 607 677 304 553 787 103 622 334 742 230 600 927 520 92 955 288 448 892 46 1012 344 511 884 178 453 960 351 25 769 523 164 509 832 531 431 637 213 714 16 790 581 118 667 872 340 238 898 646 305 150 930 99 853 290 980 528 245 83 455 153 556 7982 393 11 967 661 255 726 484 617 144 383 737 60 1010 417 911 97 515 760 207 442 825 373 57 921 463 860 277 647 218 589 251 584 996 299 692 602 131 985 586 211 679 84 962 500 808 19 732 460 159 822 76 291 749 242 422 835 317 767 435 127 368 882 286 939 379 613 525 902 77 542 944 4 716 231 610 916 552 193 626 36 756 135 846 670 348 781 179 529 449 1017 52 330 784 404 986 504 248 908 444 147 999 505 313 896 113 487 813 536 101 668 157 804 652 387 3 476 639 54 820 565 362 727 161 952 297 862 481 324 94 1001 705 936 226 718 427 188 974 249 585 390 745 44 594 893 508 216 534 119 831 264 915 547 21 858 513 88 560 923 356 142 664 816 363 535 389 627 130 763 406 606 272 1005 445 177 702 971 414 51 886 796 79 989 519 332 933 109 785 219 844 630 293 81 789 608 300 341 693 310 863 35 498 702 367 679 8 424 870 569 342 202 1022 880 457 181 674 441 817 174 959 301 578 990 151 451 931 698 107 232 956 557 117 1019 280 618 78 754 209 374 687 806 23 407 583 603 10 775 491 227 762 398 889 339 828 543 115 284 543 850 322 419 709 319 913 491 26 663 186 712 50 903 465 978 522 129 951 1003 258 812 96 428 841 247 943 443 604 308 736 68 345 786 447 70 649 204 574 970 287 700 479 105 1013 195 421 881 562 215 571 690 354 934 483 154 765 61 577 848 350 757 550 141 480 1002 90 222 861 20 747 370 546 991 331 175 684 12 963 382 799 302 612 580 440 634 312 897 124 410 871 628 289 811 244 597 30 730 260 912 173 1023 89 595 472 779 37 502 937 148 586 454 941 199 879 346 665 397 795 234 950 279 724 217 585 401 905 102 599 343 669 31 834 143 461 706 5 659 366 983 85 748 326 818 426 981 121 385 5 823 494 176 907 27 518 891 104 992 220 539 721 425 241 925 657 265 696 353 563 797 252 624 196 501 768 149 335 810 597 140 517 888 93 997 146 458 964 208 788 33 479 876 489 13 976 1020 347 203 733 551 412 707 87 571 298 926 365 110 948 544 184 39 620 803 384 17 857 276 90 474 827 155 532 752 270 717 360 722 437 123 914 656 229 746 376 69 605 423 1015 235 548 80 774 254 883 533 266 503 942 163 530 979 282 686 48 869 4242 836 323 596 65 672 987 98 400 619 842 132 776 212 729 569 187 388 995 413 838 358 180 570 814 29 327 640 467 954 369 106 917 572 18 946 271 772 456 738 246 1006 512 899 1 315 794 455 555 236 801 197 532 43 901 137 482 681 190 380 715 571 166 878 59 953 488 338 1016 512 372 555 935 31 601 864 267 975 434 592 329 695 171 735 111 694 224 819 296 783 450 126 771 55 725 136 1021 377 527 561 874 311 969 58 635 214 993 556 243 676 306 805 545 28 868 259 468 611 160 753 416 713 41 364 940 399 873 206 418 778 281 945 32 852 493 256 833 114 894 658 152 609 91 645 919 40 590 168 731 240 660 928 71 582 185 471 824 295 988 492 275 723 438 548 430 984 125 524 357 1014 403 701 47 758 537 167 843 15 965 751 86 589 136 791 625 116 845 262 961 223 409 710 355 553 210 253 809 395 904 14 292 761 490 538 139 558 895 82 1009 261 750 497 636 169 673 469 957 446 67 920 349 734 237 793 433 575 63 890 38 966 269 815 191 728 309 521 866 2 506 615 134 938 495 198 770 477 573 108 641 378 998 172 598 420 973 274 682 303 854 680 391 233 851 411 932 22 554 329 100 773 189 837 34 744 162 9 521 1008 74 699 337 809 200 332 704 361 631 325 918 394 538 906 333 182 777 496 120 514 654 910 263 1018 75 720 478 138 800 375 740 529 257 875 439 982 318 49 587 205 807 250 593 977 285 840 114 922 588 42 691 158 766 486 885 352 523 949 24 459 741 507 650 170 392 947 239 856 402 688 145 780 112 678 381 887 95 56 994 452 802 294 666 526 66 288 968 470 642 196 826 307 510 485 278 711 72 755 128 1011 462 821 371 7 929 415 616 165 764 855 576 221 958 429 614 328 739 183 701 562 316 849 73 1004 549

TABLE #5 Transfer Function Table to Convert 10-bit Values to 8-bit Values | *0 *1 *2 *3 *4 *5 *6 *7 *8 *9 *10 *11 *12 *13 *14 *15  (0) 0 1 2 3 3 4 5 6 6 7 8 9 10 10 11 12  (32) 25 26 26 27 28 29 30 30 31 32 33 33 34 35 36 36  (64) 49 50 50 51 52 53 53 54 55 56 56 57 58 58 59 60  (96) 72 73 73 74 75 75 76 77 77 78 79 79 80 81 81 82 (128) 93 94 94 95 95 96 97 97 98 99 99 100 100 101 102 102 (160) 112 113 113 114 114 115 115 116 116 117 117 118 118 119 120 120 (192) 129 129 130 130 131 131 132 132 133 133 133 134 134 135 135 136 (224) 143 144 144 144 145 145 146 146 146 147 147 148 148 148 149 149 (256) 156 156 156 157 157 157 158 158 158 159 159 159 160 160 160 161 (288) 166 167 167 167 167 168 168 168 169 169 169 170 170 170 170 171 (320) 176 176 176 176 177 177 177 177 178 178 178 179 179 179 179 180 (352) 184 184 185 185 185 185 186 186 186 187 187 187 187 188 188 188 (384) 193 193 193 194 194 194 195 195 195 196 196 196 196 197 197 197 (416) 201 201 201 201 201 202 202 202 202 203 203 203 203 203 204 204 (448) 207 208 208 208 208 208 209 209 209 209 209 210 210 210 210 210 (480) 213 214 214 214 214 214 214 215 215 215 215 215 215 216 216 216 (512) 219 219 219 219 219 219 220 220 220 220 220 220 220 221 221 221 (544) 223 223 224 224 224 224 224 224 224 224 225 225 225 225 225 225 (576) 227 227 227 228 228 228 228 228 228 228 228 228 229 229 229 229 (608) 231 231 231 231 231 231 231 231 232 232 232 232 232 232 232 232 (640) 234 234 234 234 235 235 235 235 235 235 235 235 235 235 235 235 (672) 236 236 236 236 237 237 237 237 237 237 237 237 237 237 237 237 (704) 238 238 238 238 238 239 239 239 239 239 239 239 239 239 239 239 (736) 240 240 241 241 241 241 241 241 241 241 241 241 241 241 241 241 (768) 243 243 243 243 243 243 243 243 243 243 243 243 243 243 244 244 (800) 245 245 245 245 245 245 245 245 245 245 245 245 245 245 245 246 (832) 246 247 247 247 247 247 247 247 247 247 247 247 247 247 247 247 (864) 248 248 248 248 248 248 248 248 248 248 248 249 249 249 249 249 (896) 249 249 249 249 250 250 250 250 250 250 250 250 250 250 250 250 (928) 251 251 251 251 251 251 251 251 251 251 251 251 251 251 251 251 (960) 252 252 252 252 252 252 252 252 252 252 252 252 252 252 252 252 (992) 253 253 253 253 253 253 253 253 253 254 254 254 254 254 254 254 *16 *17 *18 *19 *20 *21 *22 *23 *24 *25 *26 *27 *28 *29 *30 *31  (0) 13 13 14 15 16 16 17 18 19 20 20 21 22 23 23 24  (32) 37 38 39 39 40 41 42 42 43 44 45 45 46 47 48 48  (64) 61 61 62 63 63 64 65 66 66 67 68 68 69 70 70 71  (96) 83 83 84 85 85 86 87 87 88 89 89 90 90 91 92 92 (128) 103 103 104 104 105 106 106 107 107 108 109 109 110 110 111 111 (160) 121 121 122 122 123 123 124 124 125 125 126 126 127 127 128 128 (192) 136 137 137 138 138 138 139 139 140 140 141 141 142 142 142 143 (224) 150 150 150 151 151 152 152 152 153 153 153 154 154 155 155 155 (256) 161 161 162 162 162 163 163 163 164 164 164 165 165 165 166 166 (288) 171 171 172 172 172 172 173 173 173 174 174 174 174 175 175 175 (320) 180 180 180 181 181 181 181 182 182 182 183 183 183 183 184 184 (352) 188 189 189 189 190 190 190 190 191 191 191 191 192 192 192 193 (384) 198 198 198 198 198 198 198 199 199 199 199 200 199 200 200 200 (416) 204 204 205 205 205 205 205 206 206 206 206 206 207 207 207 207 (448) 210 211 211 211 211 211 212 212 212 212 212 213 213 213 213 213 (480) 216 216 216 217 217 217 217 217 217 218 218 218 218 218 218 219 (512) 221 221 221 221 222 222 222 222 222 222 222 223 223 223 223 223 (544) 225 225 226 226 226 226 226 226 226 226 227 227 227 227 227 227 (576) 229 229 229 229 229 230 230 230 230 230 230 230 230 230 231 231 (608) 232 232 232 233 233 233 233 233 233 233 233 233 233 233 234 234 (640) 235 236 236 236 236 236 236 236 236 236 236 236 236 236 236 236 (672) 237 237 237 237 237 238 238 238 238 238 238 238 238 238 238 238 (704) 239 239 239 240 240 240 240 240 240 240 240 240 240 240 240 240 (736) 242 242 242 242 242 242 242 242 242 242 242 242 242 242 242 243 (768) 244 244 244 244 244 244 244 244 244 244 244 244 244 244 245 245 (800) 246 246 246 246 246 246 246 246 246 246 246 246 246 246 246 246 (832) 247 247 247 247 247 248 248 248 248 248 248 248 248 248 248 248 (864) 249 249 249 249 249 249 249 249 249 249 249 249 249 249 249 249 (896) 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 251 (928) 251 251 251 251 251 251 251 251 251 251 251 252 252 252 252 252 (960) 252 252 252 252 253 253 253 253 253 253 253 253 253 253 253 253 (992) 254 254 254 254 254 254 254 254 254 254 255 255 255 255 255 255

TABLE #6 8-bit Adjusted 32 × 32 Threshold Array-From 10-bit Unadjusted Array 250 165 226 252 176 248 110 245 161 249 212 35 235 130 223 241 89 219 242 49 235 144 226 206 233 96 237 254 160 248 48 176 198 248 129 213 250 193 253 41 247 217 133 199 239 186 244 231 237 171 224 244 77 232 179 241 146 230 251 220 69 252 145 207 249 36 254 182 219 249 122 208 252 184 20 243 232 114 218 246 271 204 233 138 239 13 244 228 87 236 248 181 149 249 235 171 106 251 74 248 167 253 221 152 246 211 108 225 244 196 9 252 236 155 240 214 232 103 193 240 46 254 201 250 73 239 242 136 206 246 190 44 250 210 248 163 235 141 237 154 228 253 170 237 230 95 253 228 138 236 63 252 217 245 15 240 210 111 246 58 167 241 150 202 247 175 243 205 92 188 249 166 251 191 231 221 250 58 223 251 3 239 146 231 250 224 129 232 28 242 97 247 236 183 243 122 233 208 254 40 178 244 198 253 217 153 250 207 104 253 218 174 249 83 215 245 222 75 236 110 245 235 194 3 213 234 42 246 226 187 240 113 251 169 248 214 177 70 254 238 251 144 239 203 127 252 153 237 195 241 34 229 249 218 140 222 87 246 258 250 224 16 248 219 66 225 250 185 102 236 246 187 222 194 233 94 242 198 231 161 254 207 121 238 252 200 39 249 244 60 253 220 179 251 81 244 141 247 233 158 61 244 231 170 181 238 173 248 27 216 238 188 237 6 202 248 226 181 133 255 249 209 123 236 206 246 120 252 170 227 253 107 208 251 238 79 146 252 225 86 255 164 232 59 242 137 190 237 245 18 199 228 230 8 243 215 144 242 197 249 181 246 223 85 165 234 247 176 201 239 175 250 229 20 236 126 239 39 250 211 252 220 34 251 254 156 245 72 203 247 152 251 206 230 172 240 52 182 244 207 53 235 134 227 252 166 238 213 78 254 130 202 249 236 139 227 237 185 251 214 109 242 47 227 247 184 242 224 101 213 254 68 142 248 16 241 189 224 253 179 120 237 10 242 192 245 170 231 228 206 233 173 249 90 199 248 233 167 245 151 238 23 240 157 250 119 255 57 229 212 243 29 217 251 105 226 209 251 132 249 183 236 197 244 147 251 163 240 140 228 198 250 76 230 182 236 24 247 102 210 238 4 236 188 253 64 241 177 246 203 253 89 193 5 246 216 121 250 21 220 249 77 253 142 223 239 203 150 250 236 159 238 184 226 244 154 232 196 217 243 106 180 245 230 100 219 249 70 253 104 209 242 136 244 26 228 249 215 10 252 255 183 134 240 224 200 238 66 236 169 250 188 81 251 223 125 30 232 245 191 13 248 162 250 212 246 109 222 242 160 239 186 239 205 90 250 235 145 241 191 45 230 202 254 148 235 61 243 193 5 246 216 121 260 21 220 249 77 243 142 223 239 203 150 250 236 249 238 184 226 244 154 232 196 217 243 106 180 245 230 100 219 249 70 253 104 209 252 136 244 26 228 249 215 10 252 255 183 134 240 224 200 238 66 238 169 250 188 81 251 223 125 30 232 245 193 13 248 162 250 212 246 190 222 242 160 239 186 239 205 90 250 236 145 241 191 45 230 202 254 148 235 61 243 155 249 222 159 217 251 114 221 252 164 237 37 248 210 247 176 229 50 236 253 73 198 232 247 95 243 138 240 225 126 194 253 200 247 186 123 227 245 23 177 234 211 251 139 79 250 227 14 251 161 243 209 241 152 254 219 249 1 174 244 209 235 148 245 131 233 33 350 99 214 237 128 192 239 223 115 249 53 251 215 180 254 219 190 225 251 63 230 248 159 252 205 229 178 238 118 240 82 238 143 246 169 244 208 92 743 42 240 98 255 291 221 225 248 173 252 45 233 139 253 226 151 237 172 245 223 22 248 157 211 231 112 242 201 239 32 187 251 197 248 135 201 243 164 251 25 247 216 136 247 174 249 236 107 231 68 235 250 31 229 116 240 160 236 251 54 228 125 212 246 168 243 215 162 240 205 224 204 253 91 220 185 254 198 238 36 242 222 116 247 12 252 241 65 229 180 244 232 85 247 158 252 143 199 239 185 235 137 155 247 196 250 11 167 242 215 234 100 225 249 62 254 157 241 218 233 117 236 211 252 207 51 260 183 240 148 244 204 227 48 43 253 208 246 168 236 221 50 166 252 212 234 131 246 172 218 214 163 239 55 242 93 254 210 246 189 6 251 200 232 115 242

TABLES #4–6 provide an example of a preferred methodology to correct for improved visual perception an unadjusted 10-bit stochastic threshold array and to convert that information to an adjusted 8-bit threshold array. TABLE #4 illustrates a 32×32 stochastic threshold array, in which each of the array elements has a 10-bit value in the range of 1–1023. As in the previous example, the numeric value zero (0) is not used in any of these array elements. Since there are 1024 array locations, and 1024 (or more precisely 1023) possible numeric values, there should be a single array element location for each particular numeric value in this range. (Obviously, one of the numbers must be represented twice within this array.) Since this array is unadjusted, if a printer were to take this array's values and directly use that for its gray level halftoning, a curve such as the one at 102 in FIG. 2 would likely result as the printed response of light intensity versus gray level in which the gray levels range from 1–1023.

TABLE #5 is a look-up table that is used to convert the 10-bit values of an unadjusted array (i.e., the array of TABLE #4) to adjusted 8-bit numeric values. TABLE #6 is the resulting adjusted threshold array, which uses 8-bit precision having values ranging between 1–255. TABLE #5 starts with values in the range of 1–1023, and therefore, requires a 32×32 array for storing this look-up table. The final adjusted 8-bit array of TABLE #6 is also 32×32 in size, however, the numeric values of the array elements of TABLE #6 are only 8-bit values ranging between 1–255.

As can be seen by an inspection of TABLE #5, there are no skipped or missing numeric values in the range of 0–255 among the array elements in TABLE #5. There are, of course, duplicate numeric values for more than one array location in many cases, especially in the larger values in the darker gray levels. A histogram of output values for the final 8-bit adjusted array depicted in TABLE #6 is illustrated on FIG. 10. As can be seen by viewing FIG. 10, every threshold value has at least one occurrence for this 32×32 array.

TABLES #4–6 are used in a similar manner as were the tables in the 8-bit example of TABLES #1–3. For example, in TABLE #4, the numeric value for the lower left-hand corner array element is equal to “31.” This value “31” corresponds to the 10-bit range of 0–1023. The look-up table depicted in TABLE #5 shows this array location in the upper right-hand corner of this TABLE #5. As can be seen by inspecting the look-up table on TABLE #5, the converted, adjusted numeric value for this array location is equal to “24.”

The final result is illustrated in TABLE #6 by inspecting the lower left-hand corner array element location, which has a numeric value of “24.” Thus, the 10-bit unadjusted value of “31” becomes an adjusted 8-bit value of “24,” utilizing the principles of the present invention and the look-up table conversion methodology. One key aspect of this methodology is the use of a numeric precision in the unadjusted array that is greater than the numeric precision in the final adjusted array. In the example of TABLES #4–6, herein, the precision of the unadjusted array was 10-bits, which provides a numeric range between zero (0) and 1023. At the same time, the precision of the final adjusted array was 8-bits, ranging numerically between zero (0) and 255. This not only allows a more uniform histogram of threshold values (as illustrated in FIG. 10), but also allows for much finer gray level resolution that more perfectly emulates the human perceptual levels of increasing lightness or darkness for any given color. This last concept is illustrated in TABLE #7.

TABLE 7 Number of Number of Number of Perceptual Normalized Dots 8-bit Dots 10-bit Dots 8-bit Level 0–255 Level Unadjusted Unadjusted Adjusted  0 0 0 0 0  1 0.25 16  2 0.5 32  3 0.75 48  4 1 64 64 16  5 1.25 80  6 1.5 96  7 1.75 112  8 2 128 128 32  9 2.25 144 10 2.5 160 11 2.75 176 12 3 192 192 48 13 3.25 208 14 3.5 224 15 3.75 240 16 4 256 256 48 17 4.25 272 18 4.5 288 19 4.75 304 20 5 320 320 64 21 5.25 336 22 5.5 352 23 5.75 368 24 6 384 384 80 25 6.25 400 26 6.5 416 27 6.75 432 28 7 448 448 96 . . . . . . . . . . . . . . . 1015  253.75 16,240 1016  254 16,256 16,256 16,320 1017  254.25 16,272 1018  254.5 16,288 1019  254.75 16,304 1020  255 16,320 16,320 16,320 1021  255.25 16,336 1022  255.5 16,352 1023  255.75 16,368

In TABLE #7, the left-hand column represents a theoretical perceptual level of lightness versus darkness, ranging between the values of 0–1023. Since the human eye cannot actually discern anywhere close to that number of perceptual levels, the next column to the right on TABLE #7 provides a “normalized” perceptual level in the range of 0–255. This is achieved by merely dividing by four the numeric values of the perceptual level in the left-hand column. For example, the perceptual level 9 becomes 2.25 on the normalized perceptual level column.

Even this normalized perceptual level column is not entirely accurate with respect to possible human perceptual level sensitivities. In general, human beings can perceive only approximately one hundred different levels of light intensity or darkness, and that is one reason that the CIELAB L* scale ranges between zero (0) and one hundred (100). On the normalized 0–255 level column of TABLE #7, these levels run from zero (0) through 255, which really more closely approximates an 8-bit gray scale darkness or lightness level. Of course, the key idea here is to use an adjusted gray scale level so that the linearly increasing numeric values along the normalized level column will approximate the perceptual level sensitivity of the human eye.

It will be understood that the tables provided in this document (i.e., TABLES #1–6) were provided as 32×32 threshold arrays, which had a total of 1024 possible array element locations. This is not necessarily a preferred array size for a tiling-type threshold array to be used in an actual printer. In fact, it is preferred to use a much larger array, one having a threshold array that is 128×128 elements in size. This provides a total number of elements or pixel locations of 16,384, which is equal to 2¹⁴. If 8-bit element values are used to make up this 128×128 array in memory, then a total of 16,384 bytes will be required to represent the entire array. As with other prior art halftoning techniques, it is preferred to use the threshold array in a tiling manner over the entire bitmap that is to be printed.

The values in TABLE #7 in the three right-hand columns refer to the number of dots that will have a particular numeric value within a threshold array that is 128×128 in size. The middle column refers to the number of dots that would be used in each position for an 8-bit unadjusted stochastic threshold array. For example, using the normalized scale, a value of three (3) means that there will be 192 dots that will be printed for that particular gray level of intensity. Of course, this unadjusted scale would ultimately lead to a printing response similar to that depicted by the curve 102 in FIG. 2. Each gray level increase adds 64 more dots to the next threshold array level.

The fourth column from the left shows the number of dots that would be printed for each gray level using a 10-bit unadjusted stochastic threshold array. Since there is greater precision to be utilized, there will only be an increase of sixteen additional dots per level change, although on the normalized level scale of the second column, each integer increase would also provide a 64-dot level increase as one increases the normalized gray level, from integervalue to the next integer value.

This greater precision available in a 10-bit unadjusted array can be used to advantage by applying the principles of the present invention. Since the 10-bit unadjusted array has one part out of 1024 precision, the look-up table concept can be used to map the lighter gray level values to provide an adjusted 8-bit array that will essentially have the same precision of the original 10-bit unadjusted array. In other words, the final resulting 8-bit array (which would normally only have a precision of one part of 256) can effectively have a much better precision of one part out of 1024. This is demonstrated by inspecting the fifth column (i.e., the right-hand column) of TABLE #7.

For example, if the normalized level of three (3) is to be printed, using the adjusted threshold array will result in forty-eight (48) dots being printed instead of the unadjusted value of 192. This will obviously provide a much lighter shading for the preferred printer's halftoning technique, but this is precisely what is needed to correct the non-linear printer response, such as the curve 102. The resulting perceptual response of the right-hand adjusted column is much closer to the straight line 100 on FIG. 2. In fact, the adjusted response will be precisely along line 100, at least within the precision of the 10-bits that were provided in the initial unadjusted threshold array. Of course, that precision is only one part out of 1024, which means there is about a 1/10^(th)% error as a maximum deviation from the preferred straight line 100, as would be seen on a graph of L* versus gray level (similar to FIG. 2). Naturally, if the unadjusted threshold array were to have a greater precision (such as 11-bit or 12-bit precision), then the final output of the 8-bit adjusted array could have even finer differentiations between numbers of dots being printed at the normalized levels, and could have even less error as compared to the ideal target response along line 100 of FIG. 2, for example.

This concept has been thoroughly tested by the inventors, and the 10-bit precision available using the exact teachings of the present invention provide a very close match to the perfect target response for a printer's output, and any small fractional percentage error would be essentially indiscernible by the normal human eye.

The middle column of TABLE #7 provides a result that is essentially equivalent to the 32×32 unadjusted 8-bit array illustrated in TABLE #1, with the understanding that the 32×32 array only has a total of 1024 possible array element locations, whereas the number of dots depicted on TABLE #7 represent a 128×128 array having a total possible number of array elements of 16,384. In a similar manner, the fourth column from the left on TABLE #7 provides a result that is essentially equivalent to providing a 10-bit unadjusted array such as that depicted in TABLE #4 (again with the same understanding that the number of dots is different for the smaller 32×32 threshold array of TABLE #4). Finally, the number of dots of the 8-bit adjusted column of TABLE #7 along the right-hand column provides a result that is essentially equivalent to the adjusted array illustrated in TABLE #6, which exhibits the characteristics of the histogram depicted on FIG. 10. As discussed above, this histogram of threshold values illustrates clearly that a more uniform and linear result is provided by using a 10-bit unadjusted stochastic threshold array as the starting point as compared to merely using an 8-bit unadjusted stochastic threshold array. Since all of the threshold values are covered by the array of TABLE #6, it can be seen that a precision greater than 10 bits may not provide an important enough improvement to warrant the extra complexity and memory location requirements that would need to be provided to use a greater precision starting array.

In order to generate corrected data for the adjusted threshold array that is based upon an unadjusted stochastic threshold array (such as that depicted in TABLE #4), the printer must calculate a series of scaled lightness levels (i.e., gray levels) that will be entered into the adjusted threshold array at run time, once the printer receives a print job from a host computer. FIG. 11 illustrates a flow chart that depicts the important logical operations used by the methodology of the present invention to perform these tasks.

The first step in FIG. 11 is step 152 where the light intensity is measured for each square that was printed by the particular printer of interest, and this light intensity data is then measured, as described hereinabove with respect to FIG. 4. After that has been accomplished, a step 400 develops the parameterized transfer function, f(x)—i.e., the set of “transfer function equations”—that fits the data derived above in step 152. Of course, the data being referred to at this point is similar to the curve 102 on FIG. 2, or one of the other actual printer response curves as illustrated on FIG. 3, i.e., curves 112 or 122.

In performing this step 400, the type of equation or equations must be determined that will match up to (or “fit”) the actual data of the printer response curve. Once the type of equation for a particular range of gray scale values is determined, the precise coefficients must now be determined. Of course, in actuality, the determination of coefficients and type of equation will likely be first determined before the range of gray scale values is selected for representation by this particular equation that is derived at this step 400. Obviously, a large number of iterations will be needed to derive the actual equations, and the number of iterations will also depend upon the attempted precision that is being sought. The greater the number of bits that represents the initially-provided unadjusted threshold arrays (e.g., 10-bit data or 8-bit data), the greater the useful precision that may be obtained. Floating point numbers could also be used in the unadjusted threshold arrays, but such use of floating point numbers would defeat some of the inventive purposes of diminishing processing time at run time and minimizing storage space in non-volatile memory (e.g., ROM) of the printer.

Once the parameterized transfer function f(x) has been developed, at run time the transfer function equations (i.e., the f(x) parameterized transfer function) can be sampled, starting at a step 410. In the flow chart of FIG. 11, the variable “T” represents the tone level that will be used in a threshold array. The tone level “T” will have a numeric range from zero through the maximum decimal or binary number that can be defined with a particular number of binary digits in a memory location or in a register. For example, if 8-bit data is to be used, then the range of numeric values for “T” will be 0–255. On the other hand, if 10-bit data is used, then the numeric range of values for “T” will be 0–1023. At step 410, the value of “T” is set to zero (0). In the preferred embodiment, “T” in the unadjusted threshold array will have the range 0–1023, since the array elements are represented by 10-bit numbers. If the unadjusted array were to use array elements that are represented, for example, by 8-bit numbers, then “T” would have a range of 0–255.

A step 412 now determines whether or not the current value of “T” is equal to its maximum possible value. Of course, the answer will be NO at this point, since “T” was just set to zero (0). That being the case, the logic flow is directed to a step 414 that calculates a lightness value, essentially a value for L*, which is equal to the function of “x,” f(x). In this instance, f(x) is equal to a function of {T·(tone levels/max)}. The quantity “tone levels” represents the maximum number of gray levels that will be used in the final adjusted threshold array, and is not dependent upon the precision of the numeric elements of the adjusted array, or the unadjusted threshold array for that matter. It is preferred that “tone levels” be set to a value of 255, which provides more than enough precision to give a smooth number of perceived tone levels (i.e., more levels that can be perceived by a human eye), and further the maximum value of 255 can be represented by a single 8-bit byte in memory. In addition, the preferred value for “max” is 1023, which represents the maximum (base 10) numeric value of a 10-bit binary number. In effect, this part of the equation f(x) is used to “normalize” the data from 1024 steps (at 10-bit precision) from 0–1023, to 256 steps (but still at 10-bit precision) from 0–255. This is similar to the two left-hand columns illustrated above in TABLE #7, in which the number of steps is 1024 in both cases, but the second column describes these steps as being in the range of 0–255.75.

The function “f(x)” used in step 414 gives values for L* in the range of 0–100, in which 0=pure black and 100=pure white. The f(x) values derived in this step 414 represent a multiple sampling of the actual printer response curve (such as curve 102 of FIG. 2) for a particular combination of printer color and print media. If, for example, the precision of the unadjusted array is 10-bits, then f(x) will sample the printer response curve 1024 times to create that many uncorrected values of L* to be used in further steps of the flow chart of FIG. 11. After the first pass has been accomplished, a step 416 increments the value of “T,” and the logic flow is returned to decision step 412 to sample the next value at the next incremental tone level.

Once the entire range of tone levels has been sampled and L[T] has been calculated for each of these tone levels, then the result at decision step 412 will become YES, and the logic flow will be directed to a step 418, where “T” is again set to zero (0). At this time, the methodology of the present invention will scale the data values to the appropriate range. In the earlier step 414, the preferred tone level range for “T” used 10-bit data, so the values for T ranged from 0–1023. In the following steps starting with a decision step 420, the values for “T” will be scaled to an 8-bit range of numeric values 0–255.

At decision step 420, it is determined if “T” is equal to its maximum value (i.e., of 1023, when using 10-bit data, as per this example). Of course, at this first pass the result will be NO and the logic flow is directed to a step 422, where a scaled value for the lightness level “L[T]” is calculated using the equation: {[(Smax−Smin)/(Lmax−Lmin)]·(Lmax−L[T])}+Smin. For this calculation, the values for the variable “S” are to be 8-bit precision in a preferred embodiment, so these values will range from 1–255. In other words, Smax=255, and Smin=1. In the magenta example for plain paper exhibited on FIG. 2, the maximum L* value was 94.8, whereas the minimum L* value was 46.1. In the equation provided in step 422 of FIG. 11, the value for Lmax is, therefore, equal to 94.8, and the value for Lmin is, therefore, equal to 46.1. The use of these actual maximum and minimum values of L* for a particular printer's actual printed response will tend to maximize the precision that can be obtained when using the methodology of the present invention.

Step 422 functions to maximize the precision of the L* values that are of particular interest for this combination of printer color and print media. There will always be a maximum and minimum achievable L* value for any particular such combination, and these achievable maximum and minimum L* values will almost never be a zero (0) and one hundred (100). So it is preferred to concentrate solely on the actual achievable range of printed response for this combination. The general form of the equation is provided at step 422 on the flow chart of FIG. 11.

In the preferred embodiment depicted in FIG. 11, the result of the iterative process created by steps 420, 422, and 424, is to create a temporary look-up table, which preferably would be stored in the printer's RAM 15. This temporary look-up table is used to convert 10-bit uncorrected values of the elements of the unadjusted array into 8-bit corrected values of the elements for the newly-formed adjusted array, and is essentially equivalent to a Transfer Function Table that is disclosed in a commonly-assigned patent application, Ser. No. 09/441,581, filed on Nov. 17, 1999, titled “Method and Apparatus for Correcting Unadjusted Threshold Arrays for Halftoning by Use of Transfer Function Tables,” also owned by the common assignee Lexmark International, Inc., which is incorporated by reference herein. An example of such a Transfer Function Table is provided in TABLE #5, depicted hereinabove, where it is referred to as a temporary look-up table.

After step 422 creates a scaled L* lightness value, a step 424 increments the value of “T,” and decision step 420 again determines whether or not the value of “T” has reached its maximum value. The result will continue to be NO until the entire range of tone levels has been scaled, after which time the result at decision step 420 will become YES, and the logic flow will be directed to a step 430. At this point in the logic flow, the temporary look-up table has been fully generated.

Beginning at step 430, correction will be made to the unadjusted data, thereby resulting in a threshold array containing adjusted data. At step 430, a variable “R” is set equal to zero (0), and a variable “C” is also set to zero (0). The variable “R” is equivalent to the row of the adjusted array that is being calculated, and the variable “C” is equivalent to that array's column. In essence, the “R” variable is equal to the width of the unadjusted (as well as the adjusted) array, and the “C” variable is equal to height of those same unadjusted and adjusted arrays. It is preferred that the height and width of these arrays is 128×128 in size, which is the preferred size of a threshold array (or “screen”) that will be used in a tiling manner to halftone a bitmap image. Using this array size, the variable “width” is set to a value of 128, and the variable “height” also is set to a value of 128.

The logic flow is now directed to a decision step 432 which determines if the current value of “R” is less than the maximum width of the unadjusted array. At this first pass through the logic, the result will of course be YES, and a decision step 440 will determine whether or not the current value of “C” is less than the height of the unadjusted array. The result at this first pass will of course be YES, and a step 450 will now calculate the value for a particular element of the adjusted threshold array.

At step 450, the adjusted array's particular row and column element (starting with (0,0) position) is determined by calculating the scaled value of L* from the unadjusted array, at that unadjusted array's same row and column position. Using the example 32×32 threshold array provided on TABLES #4–6, at the row and column (0,0), the unadjusted array element had a value of 924, of a possible range of 0–1023 (for 10-bit data). In the temporary Transfer Function Table used to convert the 10-bit unadjusted values to 8-bit adjusted values, it can be seen that the unadjusted value of 924 will result in an adjusted 8-bit value of 250, which is the value at the (0,0) position in the adjusted threshold array of TABLE #6.

It can be easily discerned that the 10-bit data of TABLE #4 was converted to 8-bit data in TABLE #6 using the parameterized transfer function that resulted in the temporary Transfer Function Table (e.g., TABLE #5). As a second example, a relatively “light” gray level can be seen at the bottom-left position of the unadjusted 32×32 threshold array of TABLE #4, which is the row and column position (31,0), in which the unadjusted 10-bit data value is 31. From TABLE #5, it can be seen that this unadjusted 10-bit value is to be adjusted to a numeric value of 24 in the 8-bit range of the adjusted array. The final result can be viewed in the bottom-left corner of TABLE #6, in which the numeric value of 24 is exhibited.

After a particular row and column element has been scaled, thereby creating the adjusted value in its proper location in the adjusted threshold array, a step 452 now increments the column value variable “C,” and the logic flow is directed back to decision step 440. This inner DO-loop continues until all of the columns have been operated upon for this particular row, at which time the result at decision step 440 will become NO. When that occurs, a step 440 will reset the value for “C” to zero (0), and will increment the value for the row variable “R” by one (1). After that occurs, the logic flow is directed back to the decision step 432 to determine if the value of “R” is still less than the width of the array. The result at this decision step 432 will remain YES until all columns and all rows have been operated upon. When that occurs, the result at decision step 432 will become NO, and this routine will be finished so that the microprocessor can return to performing other tasks as the logic flow is directed to a step 434, labeled as “Done.”

It will be understood that equations other than the exact ones provided on FIG. 11 could be used without departing from the principles of the present invention, while still obtaining the desirable results of the present invention. Furthermore, as an alternative embodiment, the transfer function equations can be sampled one row and column position at a time to directly derive the adjusted threshold array values without generating a temporary look-up table or “Transfer Function Table” of any form. Instead, each 10-bit data element of the unadjusted threshold array will be compared to its L* position on the uncorrected actual printer response curve (such as curve 102 on FIG. 2), and that particular value of L* will be used to intersect the ideal target response curve (i.e., line 100 on FIG. 2) to determine its proper gray level numeric value. Once this value is determined, it will be placed into the same row and column position in the adjusted threshold array.

Since a temporary look-up table is not needed in this alternative methodology, a certain amount of space in the printer's RAM would be saved that otherwise would need to be temporarily allocated. However, the execution time to derive the adjusted threshold array in this manner—that is, by inspecting each numeric value of the unadjusted threshold array and then applying the correct transfer function equation for the correct range of gray scale values to calculate the corrected numeric value in the adjusted array—will likely require greater processing time as compared to the preferred methodology of generating a look-up table by creating a conversion value once time for each single possible numeric value of an array element in the unadjusted threshold array.

In this alternative embodiment, multiple calculations will be necessary for the very same numeric value in circumstances where the unadjusted threshold array is of a sufficient size, i.e., if its size requires the same threshold level numeric value in multiple array element locations. For example, if the unadjusted threshold array is 128×128 in size, and if its array element precision is 10-bits, there will be sixteen (16) dots for each threshold level. In the alternative embodiment, the mathematical calculations (using the parameterized transfer function equations) must, therefore, be performed sixteen times for each possible numeric value in the unadjusted array. To the contrary, the mathematical calculations (using the parameterized transfer function equations) must be performed only once for each possible numeric value in the unadjusted array in order to generate a temporary look-up table.

Not only do the teachings of the present invention provide a much more ideal response for the printer's printed output as compared to the ideal perceptual level, but additionally a much smaller amount of memory space is utilized as compared to conventional adjusted arrays that are stored in a printer's ROM. It will be understood that, even a printer that may store its adjusted threshold arrays in a memory device other than ROM (e.g., such as a hard disk drive) will still require these adjusted threshold arrays to ultimately be downloaded into the printer's RAM. Thus, the printer must spend processing time and real time to upload information from the hard disk drive (in this example) into RAM, which greatly increases its processing time. Such a printer will either be very inefficient if this processing time must occur at the beginning of each print job, or such a printer must download into its RAM all of the needed adjusted threshold arrays upon initialization, which means that a large portion of its RAM must be allocated all of the time just to hold these adjusted threshold arrays. To the contrary, the present invention only stores the adjusted threshold arrays in RAM at run time for each individual print job, and only stores those adjusted threshold arrays for the precise type of print media and the type of colors that are to be printed for that particular print job.

As an example, if a color printer were to store a set of 8-bit adjusted threshold arrays for a color printer having four different colors, each of those colors would require 16 Kbytes per threshold array. These are the four ordinary colors that, for example, would include cyan, magenta, yellow, and black. However, certain ink jet color printers can also support two further pigments known as “dilute cyan” and “dilute magenta.” Therefore, an additional threshold array is required for each dilute colorant. Furthermore, when the dilute colorants are used, a different formulation of black pigment is also used. Therefore, in addition to the four adjusted threshold arrays needed for the ordinary 4-color printing, an additional three adjusted threshold arrays are required if the dilute printing is also to be supported by a particular printer. Finally, if dilute ink printing is to be supported, there will also be required an additional threshold array for ordinary cyan and ordinary magenta colors when using the dilute ink cartridges. This now requires a total of nine different adjusted threshold arrays for any given single type of paper.

Since a printer will optimally support at least three different paper types, there will be a total of twenty-seven different unique combinations of paper versus ink type for which a unique threshold array must be generated and stored. Since each threshold array is 16K, and the total number of threshold arrays to be stored is equal to twenty-seven, the total number of bytes in memory required to store this information will be 432 Kbytes, which typically will take up space in the printer's ROM. As can be seen, this is almost one-half Mbyte of memory locations merely to hold the various threshold arrays. Of course, if true Read Only Memory is utilized, then these arrays will not be required to be downloaded into RAM for image processing by the printer when it is time to halftone an incoming print job. On the other hand, if a hard disk drive, for example, is used to store these arrays, then processing time and real time to access the hard disk drive will be required to download the data from the hard disk, and RAM space must be then allocated to hold the appropriate arrays.

When using the principles of the present invention, the example of the 10-bit unadjusted stochastic threshold array as the starting point is implemented using much less memory space. For example, a single set of unadjusted 10-bit threshold arrays are to be stored in ROM, one for each of the four normal color planes. Each 10-bit threshold array requires 20 Kbytes, which is 25% larger than a set of unadjusted 8-bit arrays that have been used in conventional printers in the past. In other words, if four threshold arrays were stored for the four ordinary colors in 8-bit precision, then each array would require 16 Kbytes, leading to a total of 64 Kbytes of ROM space required.

However, the 10-bit unadjusted threshold arrays are the preferred embodiment, and thus 80 Kbytes of ROM are required to hold those four threshold arrays. The transfer function equations are also stored in ROM, and each set of transfer function equations (i.e., for a particular combination of color and type of print media) requires only about 70 bytes of memory space in ROM. Since there are twenty-seven different combinations of colors and paper styles to be supported, there optimally would be twenty-seven (27) different sets of transfer function equations stored in ROM. This added to the 80 Kbytes of ROM holding the initial 10-bit threshold arrays provides a total requirement of about 82 Kbytes of ROM space in the printer. Of course, it is quite obvious that this is much smaller than the conventional printer's requirements that would require 432 Kbytes of ROM space to hold 8-bit adjusted arrays for the same twenty-seven combinations (and even considerably smaller than the use of Transfer Function Tables disclosed in the co-pending patent application noted hereinabove, Ser. No. 09/441,581, also assigned to Lexmark International, Inc.).

It will be understood that all of the memory size examples provided hereinabove assume that the data will be packed, as according to the principles of the present invention that were described hereinabove. Obviously, to best utilize the packed data, it must first be unpacked, preferably according to the principles described hereinabove with respect to the flow charts provided on either FIG. 6, or FIG. 8. In the preferred embodiment discussed above, when it is time (i.e., at run time) to print an incoming print job, the stochastic threshold arrays stored in ROM for the four different ordinary colors must be utilized to create the necessary adjusted 8-bit threshold arrays for a particular type of print media.

If array data is required to print four different colors (i.e., for the ordinary colors such as cyan, magenta, yellow, and black), then four different adjusted 8-bit threshold arrays must be generated and stored in the printer's RAM, such as RAM 15 on FIG. 1. Each 8-bit threshold array requires 16 Kbytes of RAM, so to print using the four ordinary colors, a total of 64 Kbytes of RAM are required. If on the other hand six colors are to be printed (e.g., if the diluted pigments are going to be used), then a total of six adjusted 8-bit threshold arrays need to be generated and stored in RAM, which would require 96 Kbytes of RAM. Even in this worst case scenario, using the principles of the present invention a total of 203 Kbytes of memory are required (i.e., including both ROM and RAM memory requirements), which is still much less than the amount required by conventional printers that use 432 Kbytes of ROM space alone. This is, of course, quite a savings of memory resources.

It will be understood that the unadjusted threshold array data and the transfer function equations data could be stored in a memory device other that ROM, such as a hard disk drive. Moreover, the principles of the present invention can be applied to any type of printer, including laser printers, ink jet printers, thermal transfer printers, copiers having electrophotographic print engines, and so on (any of which could use either ROM or a hard disk drive to store array data).

Additionally, the unadjusted threshold array data and the transfer function equations data could be stored in a non-volatile memory device (e.g., a hard disk drive) located on a host computer (such as the “input device” 24 on FIG. 1) and downloaded to the printer either upon the printer's initialization (by way of a request from the printer to the host, for example), or upon an unsolicited communication from the host computer. In this configuration, the printer itself would need only RAM volatile-type memory to hold this information, although in a realistic application it is likely that a printer would at least hold a default unadjusted threshold array and a default set of transfer function equations within its own non-volatile memory devices.

An alternative to downloading the transfer function equations into the printer's RAM memory from a host computer (as per the example in the previous paragraph) is to download these equations into a different non-volatile memory device, such as a Flash memory device or an EEPROM memory device located either within the printer, or on a replaceable cartridge. An example of this is the memory device 42 that is part of the print engine 36, in which the transfer function equations could be downloaded into this device 42 from either a host computer, or from the printer 10 itself (as will be discussed below). Another example is the memory device 62 that is mounted on a replaceable cartridge 60, in which the transfer function equations could be downloaded additionally (or only) into this device 62 from either a host computer, or from the printer 10 itself (as also will be discussed below).

One situation in which the transfer function equations could be downloaded into one or both of the memory devices 42 and 62 is to compensate for the shift in print darkness over the life of a laser printer's process cartridge (e.g., replaceable cartridge 60). It is a well-known phenomena that many (if not most) laser print engines tend to produce darker printed images as the cleaner blade gradually scrapes away the capacitively-charged outer layer of the photoconductive (PC) drum (not shown) as printed sheets are produced by the laser print engine. In this circumstance, the energy density of the PC drum (i.e., capacitance per unit area of the PC drum) gradually increases, and the toner material tends to adhere more easily, the consequence of which is more toner is applied to the print media per printed pixel or pel. Other print engine parameters may also tend to increase the darkness of the printed output image on the print media over the life of the EP process cartridge.

In the past, this gradual darker printed output has not specifically been corrected. Instead, the initial printer response curve is “overcorrected” to a certain extent, with the knowledge that the darkness rapidly changes over the first one thousand sheets that are printed using a new EP process cartridge. In this scenario, the printer response will not look similar to that of FIG. 2, which has a decidedly concave shape to its response curve 102. Instead, the printer response for a new EP process cartridge is designed to have a somewhat convex shape that remains above the desired linear response (such as the line 100 on FIG. 2) all the way across the Gray scale range. After the first one thousand sheets have been printed, the printer response curve will quickly have dropped to approximately emulate the line 100, although the actual response curve will continually change over the usage of the EP process cartridge. However, the rate of change slows considerably after the initial usage of the EP process cartridge.

For EP process cartridges sold by Lexmark International, Inc. the shape of the printer response curve will gradually look more and more like the concave shape of curve 102. In other words, the endpoints at Gray scale values of zero (0) and 255 will not significantly change, and the shape itself of the response curve is what changes over usage life of the EP process cartridge. For EP process cartridges sold be other printer manufacturers, not only does the shape of the curve change over the usage life, but also the endpoints may change (at least for the “darker” endpoint at a Gray scale value of 255).

In either case discussed above, it is possible to attempt to compensate for the gradual darkness increase by use of the transfer functions utilizing the principles of the present invention. The printer designer must determine the printer response of a typical EP process cartridge over its usage life, and then decide at what usage intervals a correction should be made. This is precisely where the memory device 62 mounted on the EP process cartridge 60 can be effectively used, since each style of EP process cartridge may have a different change in printed darkness over its life, and this information can be easily stored in a non-volatile memory device, such as Flash or NVRAM (such as an EEPROM), or even in a write only, read often memory device such as an EPROM. This information can be transferred into the printer 10 upon command by the printer, preferably upon the printer's initialization.

The information about a particular EP process cartridge can be stored in various places within printer 10. It can be stored in RAM 15, so that it may be manipulated in any desired manner, however, it also will probably be stored in a non-volatile memory device within the printer so that this information is not lost upon de-energization of the printer. This EP process cartridge information can be stored in the printer's main memory system, such as at the Flash memory 52, the NVRAM 26, or the hard disk drive 50. In addition, or alternatively (as desired), this EP process cartridge information can be stored in the print engine's non-volatile memory 42. In either case, the transfer functions can perform a supplemental operation upon the adjusted threshold array (or arrays), and this supplemental operation is specifically designed to compensate for the gradual tendency for the print engine to produce a darker printed output over the life of the EP process cartridge.

The final result is to derive a new adjusted threshold array (or arrays) that will have somewhat different numeric elements depending upon the amount of previous usage of the EP process cartridge. By effectively causing the printer's response to become lighter over the usage of the EP process cartridge, the printer will also use less toner material than before, thereby providing a new benefit of a toner reservoir that produces more printed sheets while using the same amount of toner material. Another benefit is that uses of the printer will not perceive an obvious difference in print quality just after installing a new EP process cartridge. As things stand in conventional printers, a brand new EP process cartridge produces considerably lighter printed images as compared to the “old” EP process cartridge that was just removed from the same printer.

The printer response curve for a particular style of EP process cartridge (or other “pure” toner cartridge) can be mathematically described, and this information is used to generate appropriate transfer function equations that are appropriate for different usage intervals. Since the transfer function equations require very little memory space, it is possible to store multiple sets of these transfer function equations so that a new set is provided at regular usage intervals of the EP process cartridge, or a single set of transfer function equations can be provided in which EP process cartridge usage is one of the variables. The determination of actual usage can be accomplished in many ways, such as by counting the number of sheets that have been printed using a particular EP process cartridge, or by some measurement means that directly provides an indication of the remaining toner material (and by deduction, determines the amount of toner material already used). The tracking of this usage information can be controlled by the printer 10, and the usage information can be stored within the printer's memory, or perhaps within the memory device mounted on the EP process cartridge. If an EP process cartridge is removed from the printer, and later reinstalled, then it would be desirable for the printer to be able to determine how much usage this EP process cartridge had previously undergone.

It will be understood that particular combinations of print engine components and styles of EP process cartridges may cause the printed output to actually become lighter during use of the equipment. In this situation, the principles of the present invention still apply, although the transfer function equations would instead darken the printer response as the equipment is used.

The foregoing description of a preferred embodiment of the invention has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed. Obvious modifications or variations are possible in light of the above teachings. The embodiment was chosen and described in order to best illustrate the principles of the invention and its practical application to thereby enable one of ordinary skill in the art to best utilize the invention in various embodiments and with various modifications as are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the claims appended hereto. 

1. A method for generating an adjusted threshold array in an image forming apparatus, comprising: (a) providing an unadjusted threshold array at an image forming apparatus; (b) providing at least one transfer function equation at said image forming apparatus; (c) as part of image processing at said image forming apparatus, applying said at least one transfer function equation to said unadjusted threshold array to derive an adjusted threshold array for use by said image forming apparatus; and (d) receiving input image data at said image forming apparatus, and halftoning said input image data by use of said adjusted threshold array, without any intermediate transfer function modifying grayscale values of said input image data before being halftoned by said adjusted threshold array.
 2. The method as recited in claim 1, wherein said unadjusted threshold array is generated by one of: classical screening, using cluster-dot ordered dithering; stochastic screening, using cluster-dot unordered dithering; Bayer screening, using dispersed-dot ordering dithering; and stochastic screening, using dispersed-dot unordered dithering.
 3. The method as recited in claim 1, wherein said image forming apparatus comprises a printer, and said input image data comprises a print job.
 4. The method as recited in claim 3, wherein said printer derives an adjusted threshold array for only a precise printing requirement of said received print job.
 5. The method as recited in claim 4, wherein said precise printing requirement comprises a predetermined color and a predetermined type of print media.
 6. The method as recited in claim 1, wherein said unadjusted threshold array comprises a first plurality of individual elements each having a numeric value of a first predetermined precision, and said adjusted threshold array comprises a second plurality of individual elements each having a numeric value of a second predetermined precision.
 7. The method as recited in claim 6, wherein said first predetermined numeric precision comprises 8-bit integer data having a range of values from 0–255 inclusive, and said second predetermined numeric precision comprises 8-bit integer data having a range of values from 0–255 inclusive.
 8. The method as recited in claim 7, wherein said at least one transfer function equation generates a temporary look-up table having 256 elements, each of said elements having a numeric value within a range of 0–255 inclusive.
 9. The method as recited in claim 1, further comprising the step of: as part of image processing at said image forming apparatus, halftoning at least one color of said input image data by use of said adjusted threshold array.
 10. A method for generating an adjusted threshold array in an image forming apparatus, comprising: (a) providing an unadjusted threshold array; (b) providing at least one transfer function equation; (c) applying said at least one transfer function equation to said unadjusted threshold array at run time to derive an adjusted threshold array; (d) receiving input image data at said image forming apparatus; and (e) halftoning at least one color of said input image data by use of said adjusted threshold array, without any intermediate transfer function modifying grayscale values of said input image data before being halftoned by said adjusted threshold array; wherein said image forming apparatus comprises a video display, and said input image data comprises a video data stream.
 11. The method as recited in claim 10, wherein said video display comprises one of: a liquid crystal display (LCD), a light-emitting diode (LED) display, and a cathode ray tube (CRT) display.
 12. A method for generating an adjusted threshold array in an image forming apparatus, comprising: (a) providing an unadjusted threshold array; (b) providing at least one transfer function equation; (c) applying said at least one transfer function equation to said unadjusted threshold array at run time to derive an adjusted threshold array; (d) receiving input image data at said image forming apparatus; and (e) halftoning at least one color of said input image data by use of said adjusted threshold array, without any intermediate transfer function modifying grayscale values of said input image data before being halftoned by said adjusted threshold array; wherein said unadjusted threshold array comprises a first plurality of individual elements each having a numeric value of a first predetermined precision, and said adjusted threshold array comprises a second plurality of individual elements each having a numeric value of a second predetermined precision, and wherein said first predetermined numeric precision is greater than or equal to said second predetermined numeric precision.
 13. The method as recited in claim 12, wherein said at least one color comprises one of: red, green, blue, cyan, magenta, yellow, black, diluted cyan, and diluted magenta.
 14. The method as recited in claim 12, further comprising: printing said at least one halftoned color, wherein said adjusted threshold array provides a substantially linear printer response as compared to human visual perception.
 15. The method as recited in claim 12, further comprising: printing said at least one halftoned color, wherein said adjusted threshold array provides a non-linear printer response that substantially corresponds to a specific predetermined application. 